Relations among five radii of circles in a triangle,its sides and other segments

Students use GeoGebra to explore the mathematical relations among different radii of circles in a triangle (circumcircle, incircle, excircles) and the sides and other segments in the triangle. The more formal mathematical development of the relations that follows the explorations is based on known geometrical properties, different formulas relating the radii to the sides and the inequalities between the different averages. The activities described were conducted with pre-service teachers of mathematics, with empirical investigation of the relations using dynamical geometry software, and formal presentation of proofs.     

Dynamic investigation of triangles inscribed in a circle,which tend to an equilateral triangle

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner.

First, using geometrical software, we investigate four theorems that represent interesting geometrical properties, after which we present formal proofs that rest on a combination between different fields of mathematics: trigonometry, algebra and geometry, and the use of the concept of standard deviation that is taken from statistics.     

Effects of Periodic Excitation on the Flow Around a D-Shaped Cylinder at Low Reynolds Numbers

The baseline and forced flow around a bluff body with semi-elliptical D-shape was investigated by solving the 2D Navier–Stokes equations at low Reynolds numbers. A D-shape rather than the canonic circular-cylinder was selected due to the fixed separation points in the latter, enabling to study a pure wake rather than boundary-layer control. The correlation between Strouhal and Reynolds numbers, the mean drag, the lift and drag oscillations vs. the Reynolds number and wake structure were investigated and compared to experimental and numerical data. Effects of open-loop forcing, resulting from the influence of zero-mass-flux actuators located at the fixed separation points, were studied at a Reynolds number of 150. Fluidic rather than body motion or volume forcing was selected due to applicability considerations. The motivation for the study was to quantify the changes in the flow field features, as captured by Proper Orthogonal Decomposition (POD) analysis, due to open-loop forcing, inside and outside the “lock-in” regime. This is done in order to evaluate the suitability of low-order-models based on POD modes of this changing flow field, for future feed-back flow control studies. The evolution of the natural and the excited vortices in the Kármán wake were also investigated. The formation and convection regions of the vortex evolution were documented. It was found that the forcing causes an earlier detachment of the vortices from the boundary-layers, but does not affect their circulation or convection speeds. The results of the POD analysis of the near-wake flow show that the influence of the bluff body shape (“D”-shaped versus circular cylinder) on the baseline POD wake modes is small. It was found that the eigenfunctions (mode-shapes) of the POD velocity modes are less sensitive to slot excitation than the vorticity modes. As a result of the open-loop excitation, two types of mode-shape-change were observed: a mode can be exchanged with a lower-energy mode or shifted to a low energy level. In the latter case, the most energetic mode becomes the “actuator” mode. The evolution of one-slot excitation on still fluid (“Synthetic jet”) was studied and compared to published data and to “actuator” modes with external flow present. Based on the current findings, it is hypothesized that the cross-flow velocity POD modes are suitable for feedback control of wake flow using periodic excitation, due to their low sensitivity to the excitation as compared to the streamwise velocity or vorticity modes.     

Highly polar carbohydrates stack onto DNA duplexes via CH/π interactions

Carbohydrate-nucleic acid contacts are known to be a fundamental part of some drug-DNA recognition processes. Most of these interactions occur through the minor groove of DNA, such as in the calicheamicin or anthracycline families, or through both minor and major groove binders such as in the pluramycins. Here, we demonstrate that carbohydrate-DNA interactions are also possible through sugar capping of a DNA double helix. Highly polar mono- and disaccharides are capable of CH/π stacking onto the terminal DNA base pair of a duplex as shown by NMR spectroscopy. The energetics of the carbohydrate-DNA interactions vary depending on the stereochemistry, polarity, and contact surface of the sugar involved and also on the terminal base pair. These results reveal carbohydrate-DNA base stacking as a potential recognition motif to be used in drug design, supramolecular chemistry, or biobased nanomaterials.     

Valine and phenylalanine as precursors in the biosynthesis of alkamides in Acmella radicans

Acmella radicans (Asteraceae) produces at least seven alkamides, most with either an isobutyl- or phenylethyl group as the amine moiety. These moieties suggest that the amino acids valine and phenylalanine are the biosynthetic precursors of these alkamides. On the basis of labeled feeding experiments using either L-[2H8]valine or L-[2H8]phenylalanine we present evidence for the involvement of these two amino acids in the biosynthesis of (2E,6Z,8E)-N-isobutyl-2,6,8-decatrienamide (affinin) (1), (2Z,4E)-N-(2-phenylethyl)-2,4-octadienamide (2), (2E)-N-(2-phenylethyl)-nona-2-en-6,8-diynamide (3), and 3-phenyl-N-(2-phenylethyl)-2-propenamide (4). Alkamides were isolated from young A. radicans plants and analyzed by gas chromatography-mass spectrometry (GC-MS). Additionally, in cell free in vitro experiments based on isobutyl and phenylethylamide biosynthesis, using a colorimetric assay and GC-MS, valine and phenylalanine decarboxylase activities were assayed in the soluble extract of A. radicans leaves.     

Dynamic spanning without probabilities

The paper presents a non-probabilistic approach to continuous-time trading where, in analogy to the binomial option-pricing model, terminal payoffs resulting from a given trading strategy are meaningful ‘state-by-state’, i.e., path-by-path. In particular, we obtain results of the form: “If a certain trading strategy is applied and if the realized price trajectory satisfies a certain analytical property, then the terminal payoff is.…” This way, derivation of the Black and Scholes formula and its extension become an exercise in the analysis of a certain class of real functions. While results of the above forms are of great interest if the analytical property in question is believed to be satisfied for almost all realized price trajectories (for example, if the price is believed to follow a certain stochastic process which has this property with probability 1), they are valid regardless of the stochastic process which presumably generates the possible price trajectories or the probability assigned to the set of all paths having this analytical property.     

The structure, vibrational spectra and nonlinear optical properties of the L-lysine x tartaric acid complex--theoretical studies

The room temperature X-ray studies of L-lysine x tartaric acid complex are not unambiguous. The disorder of three atoms of carbon in L-lysine molecule is observed. These X-ray studies are ambiguous. The theoretical geometry study performed by DFT methods explain the most doubts which are connected with crystallographic measurements. The theoretical vibrational frequencies and potential energy distribution (PED) of L-lysine x tartaric acid were calculated by B3LYP method. The calculated frequencies were compared with experimental measured IR spectra. The complete assignment of the bands has been made on the basis of the calculated PED. The restricted Hartee-Fock (RHF) methods were used for calculation of the hyperpolarizability for investigated compound. The theoretical results are compared with experimental value of beta.     

Charged-particle multiplicity density at midrapidity in central Pb-Pb collisions at sqrt[S(NN)] = 2.76 TeV

The first measurement of the charged-particle multiplicity density at midrapidity in Pb-Pb collisions at a center-of-mass energy per nucleon pair √ S NN = 2.76 TeV is presented. For an event sample corresponding to the most central 5% of the hadronic cross section, the pseudorapidity density of primary charged particles at midrapidity is 1584 ± 4(stat) ± 76(syst), which corresponds to 8.3 ± 0.4(syst) per participating nucleon pair. This represents an increase of about a factor 1.9 relative to pp collisions at similar collision energies, and about a factor 2.2 to central Au-Au collisions at √ S NN = 2.76 TeV. This measurement provides the first experimental constraint for models of nucleus-nucleus collisions at LHC energies.     

Elliptic flow of charged particles in Pb-Pb collisions at sqrt[S(NN)] = 2.76 TeV

We report the first measurement of charged particle elliptic flow in Pb-Pb collisions at sqrt[S(NN)] =2.76 TeV with the ALICE detector at the CERN Large Hadron Collider. The measurement is performed in the central pseudorapidity region (|η|<0.8) and transverse momentum range 0.2

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