Short Disjoint Paths in Locally Connected Graphs

Chartrand and Pippert proved that a connected, locally k-connected graph is (k + 1)-connected. We investigate the lengths of k + 1 disjoint paths between two vertices in locally k-connected graphs with respect to several graph parameters, e.g. the k-diameter of a graph. We also give a generalization of the mentioned result. This research was partly done on a visit to the Institute of Systems Science of Academia Sinica (Beijing, China) under the project ME 418 of the Czech Ministery of Education. These authors are partly supported by the project LN00A056 of the Czech Ministery of Education.     

Scaling Transform and Stretched States in Quantum Mechanics

We consider the Husimi Q(q, p)-functions which are quantum quasiprobability distributions on the phase space. It is known that, under a scaling transform (q; p) → (?q; ?p), the Husimi function of any physical state is converted into a function which is also the Husimi function of some physical state. More precisely, it has been proved that, if Q(q, p) is the Husimi function, the function ?² Q(?q; ?p) is also the Husimi function. We call a state with the Husimi function ?² Q(?q; ?p) the stretched state and investigate the properties of the stretched Fock states. These states can be obtained as a result of applying the scaling transform to the Fock states of the harmonic oscillator. The harmonic-oscillator Fock states are pure states, but the stretched Fock states are mixed states. We find the density matrices of stretched Fock states in an explicit form. Their structure can be described with the help of negative binomial distributions. We present the graphs of distributions of negative binomial coefficients for different stretched Fock states and show the von Neumann entropy of the simplest stretched Fock state.     

Synthesis and preliminary biological evaluations of (+)-isocampholenic acid-derived amides

The synthesis of two novel (+)-isocampholenic acid-derived amines has been realized starting from commercially available (1S)-(+)-10-camphorsulfonic acid. The novel amines as well as (+)-isocampholenic acid have been used as building blocks in the construction of a library of amides using various aliphatic, aromatic, and amino acid-derived coupling partners using BPC and CDI as activating agents. Amide derivatives have been assayed against several enzymes that hold potential for the development of new drugs to battle bacterial infections and Alzheimer’s disease. Compounds 20c and 20e showed promising selective sub-micromolar inhibition of human butyrylcholinesterase \((h\hbox {BChE})\) (\(\hbox {IC}_{50}\) values \(0.80\,\pm 0.05\) and \(0.25\,\pm 0.02\,{\upmu }\hbox {M}\), respectively).     

New Aspects of Subfitness in Frames and Spaces

This paper contains some new facts about subfitness and weak subfitness. In the case of spaces, subfitness is compared with the axiom of symmetry, and certain seeming discrepancies are explained. Further, Isbell’s spatiality theorem in fact concerns a stronger form of spatiality (T ₁-spatiality) which is compared with the T _D -spatiality. Then, a frame is shown to be subfit iff it contains no non-trivial replete sublocale, and the relation of repleteness and subfitness is also discussed in spaces. Another necessary and sufficient condition for subfitness presented is the validity of the meet formula for the Heyting operation, which was so far known only under much stronger conditions.     

Alkyl glycosides as potential anti-<Emphasis Type="Italic">Candida albicans</Emphasis> growth agents

Candida infections are becoming increasingly prevalent and many clinical isolates are resistant to common azole derivatives treatment. Accordingly, the capacity of a series of 19 alkyl glycosides, mainly mannosides and glucosides but also a cellobioside with aglycone chain-length from C-6 to C-20, to inhibit the growth of laboratory and clinically isolated strains of Candida albicans, was investigated. The study showed that only glycosides with the C-10 and C-12 aglycones were effective growth inhibitors of both types of Candida, strains, whose metabolic activity was also significantly reduced as revealed by an XTT assay.     

Repetitive inductions of bioluminescence of <Emphasis Type="Italic">Pseudomonas putida</Emphasis> TVA8 immobilised by adsorption on optical fibre

Physico-chemical models of the interactions of cells with solid surfaces, which use contact angles and zeta potentials, indicated more facile adsorption of cells of Pseudomonas putida TVA8 on the quartz surface after its treatment with 3-aminopropyltriethoxysilane (APTES). A whole-cell optical fibre sensor of toluene was prepared by the adsorption of P. putida TVA8, bacteria producing light in contact with toluene on the wider end of APTES- treated quartz tapered optical fibre. The results of the measurements of luminescence from both sides of the layer of adsorbed cells were compared. Over the 135 days trial, the fibre biosensor was repetitively induced with toluene solution (26.5 mg L^?1) 68 times. The intensities of bioluminescence gradually decreased due to release of the adsorbed cells and they were only temporarily restored by the addition of nutrients. The intensities of bioluminescence induced with contaminated ground water were lower than in the mineral medium (MSM) with the same content of toluene.     

Toward a Rational Design of Highly Folded Peptide Cation Conformations. 3D Gas-Phase Ion Structures and Ion Mobility Characterization

Heptapeptide ions containing combinations of polar Lys, Arg, and Asp residues with non-polar Leu, Pro, Ala, and Gly residues were designed to study polar effects on gas-phase ion conformations. Doubly and triply charged ions were studied by ion mobility mass spectrometry and electron structure theory using correlated ab initio and density functional theory methods and found to exhibit tightly folded 3D structures in the gas phase. Manipulation of the basic residue positions in LKGPADR, LRGPADK, KLGPADR, and RLGPADK resulted in only minor changes in the ion collision cross sections in helium. Replacement of the Pro residue with Leu resulted in only marginally larger collision cross sections for the doubly and triply charged ions. Disruption of zwitterionic interactions in doubly charged ions was performed by converting the C-terminal and Asp carboxyl groups to methyl esters. This resulted in very minor changes in the collision cross sections of doubly charged ions and even slightly diminished collision cross sections in most triply charged ions. The experimental collision cross sections were related to those calculated for structures of lowest free energy ion conformers that were obtained by extensive search of the conformational space and fully optimized by density functional theory calculations. The predominant factors that affected ion structures and collision cross sections were due to attractive hydrogen bonding interactions and internal solvation of the charged groups that overcompensated their Coulomb repulsion. Structure features typically assigned to the Pro residue and zwitterionic COO-charged group interactions were only secondary in affecting the structures and collision cross sections of these gas-phase peptide ions.

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Graphical Abstract ?

     

Stability and aging of solubilized dialdehyde cellulose

Derivatization of alpha cellulose by periodate oxidation is an useful method for production of dialdehyde cellulose (DAC). Conversion of the 2,3-hydroxyl groups to a pair of aldehyde groups along with cleavage of the C2–C3 bond of anhydroglucose unit reduces crystallinity of initial material, leaving DAC soluble in water under mild conditions. Solubilization in hot water is necessary to obtain product in solution. The first part of our work confirmed that solubilization causes severe degradation of the molecular weight of the polymer. However, the chemistry and processes within these solutions are currently poorly understood. In the main part of the study, products of periodate oxidation were identified in acidic DAC solutions by NMR spectroscopy for the first time. Subsequent investigation of the acidic DAC solution's aging demonstrated that the low pH of the DAC solution considerably slows the degradation processes, namely the decrease of reactive aldehyde group content when compared to previous studies. Large increase in the molecular weight, observed after 14 days of aging, was explained by formation of intermolecular hemiacetals. Our results demonstrate that pH-stabilized aqueous DAC solutions remained active (e.g. applicable for cross-linking reactions) even several weeks after preparation, therefore reducing the need to prepare a fresh solution each time.     

DG method for numerical pricing of multi-asset Asian options—The case of options with floating strike

Option pricing models are an important part of financial markets worldwide. The PDE formulation of these models leads to analytical solutions only under very strong simplifications. For more general models the option price needs to be evaluated by numerical techniques. First, based on an ideal pure diffusion process for two risky asset prices with an additional path-dependent variable for continuous arithmetic average, we present a general form of PDE for pricing of Asian option contracts on two assets. Further, we focus only on one subclass—Asian options with floating strike—and introduce the concept of the dimensionality reduction with respect to the payoff leading to PDE with two spatial variables. Then the numerical option pricing scheme arising from the discontinuous Galerkin method is developed and some theoretical results are also mentioned. Finally, the aforementioned model is supplemented with numerical results on real market data.     

On the impact of conditional expectation estimators in portfolio theory

In this paper, we investigate the implications for portfolio theory of using conditional expectation estimators. First, we focus on the approximation of the conditional expectation within large-scale portfolio selection problems. In this context, we propose a new consistent multivariate kernel estimator to approximate the conditional expectation and it optimizes the bandwidth selection of kernel-type estimators. Second, we deal with the portfolio selection problem from the point of view of different non-satiable investors, namely risk-averse and risk-seeker investors. In particular, using a well-known ordering classification, we first identify different definitions of returns based on the investors preferences. Finally, for each problem, we examine several admissible portfolio optimization problems applied to the US stock market. The proposed empirical analysis allows us to evaluate the impact of the conditional expectation estimators in portfolio theory.