Orbits Of Maps Research Articles

In Vitro DNA/BSA Binding, Anticancer and Normal Cell Activity of Pd(II) Complexes: Substitution Behaviour and Computational Study

AbstractIn the aspect of an effective palladium based anticancer drug design, Pd(II) complexes [Pd(MAMP)Cl2], C1; [Pd(MAMP)(H2O)2]x2, C2; [Pd(MAMP)(L‐cys)]x, C3; [Pd(MAMP)(N‐ac‐L‐cys)], C4; [Pd(MAMP)(DL‐meth)]x2, C5; and [Pd(MAMP)(DL‐pen)]x, C6 (where x=ClO4−/NO3−) have been synthesised and characterised where 2‐[(methylamino)methyl]pyridine (MAMP) has been considered as carrier ligand and chloride, aqua, L‐cysteine (L‐cys), N‐acetyl‐L‐cysteine (N‐ac‐L‐cys), DL‐methionine (DL‐meth) and DL‐penicillamine (DL‐pen) are selected as leaving group. DNA as well as protein binding ability of the complexes has been investigated with CT‐DNA and BSA and the related binding parameters have been evaluated. Kinetic investigation for the reactions of Pd(II)‐diaqua complex C2 with four selected sulfur containing bio‐molecules have been carried out under pseudo first order condition. In addition, theoretical investigation has also been considered for structural optimisation, frontier molecular orbital mapping, TD‐DFT and NBO analysis. To get an insight into the cytotoxicity, the complexes have been treated on three different cancer cell lines (A549, HeLa, Hep G2) which reveal comparable anticancer activity of the reported complexes with the clinically acquainted anticancer drug Cisplatin. Very less complex initiated reactive oxygen species (ROS) with low degree of cell death in two different non‐tumour cell lines (L6 myotubes and HEK 293) indicate minimum normal cell toxicity of the complexes.

Stability in Outer space

We characterize strongly Morse quasi-geodesics in Outer space as quasi-geodesics which project to quasi-geodesics in the free factor graph. We define convex cocompact subgroups of Out (F_n) as subgroups such that an orbit map in the free factor graph is a quasi-isometric embedding, and we characterize such groups via their action on Outer space in a way which resembles the characterization of convex cocompact subgroups of mapping class groups.

Stability of Periodic Orbits and Return Trajectories of Continuous Multi-valued Maps on Intervals

Let I be a compact interval of real axis ℝ, and (I, H) be the metric space of all nonempty closed subintervals of I with the Hausdorff metric H and f : I → I be a continuous multi-valued map. Assume that P n = (x0, x1, ..., x n ) is a return trajectory of f and that p ∈ [minP n , maxP n ] with p ∈ f(p). In this paper, we show that if there exist k (≥ 1) centripetal point pairs of f (relative to p) in {(x i ; xi+1): 0 ≤ i ≤ n − 1} and n = sk + r (0 ≤ r ≤ k − 1), then f has an R-periodic orbit, where R = s + 1 if s is even, and R = s if s is odd and r = 0, and R = s + 2 if s is odd and r > 0. Besides, we also study stability of periodic orbits of continuous multi-valued maps from I to I.

The surface composition of Ceres from the Dawn mission

Ceres’ surface composition is of special interest because it is a window into the interior state and the past evolution of this dwarf planet. Disk-integrated telescopic spectral observations indicated that Ceres’ surface is hydroxylated, similar to but not exactly the same as some of the carbonaceous chondrite classes of meteorites. Furthermore, Ceres’ bulk density is low, suggesting significant water content. The Dawn mission in orbit around Ceres provided a new and much larger set of observations on the mineralogy, molecular and elemental composition, and their distributions in association with surface features and geology. The set of articles contained in this special issue is the first treatment of the entire surface composition of Ceres using the complete High Altitude Mapping Orbit (HAMO) Dawn Ceres data set and the calibrations from all the Dawn instruments. Most articles here treat the different geologic quadrangles of Ceres within the context of the entire body. There also are articles that treat global or technical topics. As a whole, these articles provide a current and comprehensive view of Ceres’ surface composition. Ceres’ surface composition shows a fairly uniform and widespread distribution of NH4- and Mg-phyllosilicates and carbonates, mixed with a dark component and with some exposures of salts and water-ice on Ceres’ surface, all indicative of the presence of aqueous alteration processes that involved the entire dwarf planet. There is also likely some contamination by low velocity infall, as seen on Vesta, but it is more difficult to distinguish this infall from native Ceres material, unlike for the Vesta case. This article introduces and provides the context for the following papers, presents a summary of the various findings, and integrates them into some general conclusions.

Digitally generating true orbits of binary shift chaotic maps and their conjugates

It is impossible to obtain chaotic behavior using conventional finite precision calculations on a digital platform. All such realizations are eventually periodic. Also, digital calculations of the periodic orbits are often erroneous due to round-off and truncation errors. Because of these errors, periodic orbits quickly diverge from the true orbit and they end up into one of the few cycles that occur for almost all initial conditions. Hence, digital calculations of chaotic systems do not represent the true orbits of the mathematically defined original system. This discrepancy becomes evident in the simulations of the binary shift chaotic maps like Bernoulli map or tent map. Although these systems are perfectly well defined chaotic systems, their digital realizations always converge to zero. In the literature, there are some studies which replace the least significant zero bits by random bits to overcome this problem.In this paper, we propose the algorithms using this simple method for digitally implementing binary shift chaotic maps. These algorithms are suitable for both software and hardware solutions, and they are also applicable with any random number generator or a repeated bit sequence. According to the type of the random number generator, either true periodic orbits or true chaotic orbits of the map are obtained. Moreover, it is shown that, utilizing topological conjugacies, obtained true orbits of binary shift chaotic maps can be used to calculate true orbits of other maps such as logistic and Chebyshev maps which are normally subject to round-off and truncation errors. The hardware implementations of binary shift chaotic maps, logistic map and Chebyshev maps have been realized on a Field Programmable Gate Array (FPGA) platform using the proposed algorithms.

On finite determinacy for matrices of power series

Let $$R=K[[x_1,\ldots ,x_s]]$$ be the ring of formal power series with maximal ideal $$\mathfrak {m}$$ over a field K of arbitrary characteristic. On the ring $$M_{m,n}$$ of $$m\times n$$ matrices A with entries in R we consider several equivalence relations given by the action on $$M_{m,n}$$ of a group G. G can be the group of automorphisms of R, combined with the multiplication of invertible matrices from the left, from the right, or from both sides, respectively. We call A finitely G-determined if A is G-equivalent to any matrix B with $${A-B} \in {\mathfrak {m}^k M_{m,n}}$$ for some finite integer k, which implies in particular that A is G-equivalent to a matrix with polynomial entries. The classical criterion for analytic or differential map germs $$f:(K^s,0) \rightarrow (K^m,0)$$ , $$K = \mathbb {R}, \mathbb {C}$$ , says that $$f \in M_{m,1}$$ is finitely determined (with respect to various group actions) iff the tangent space to the orbit of f has finite codimension in $$M_{m,1}$$ . We extend this criterion to arbitrary matrices in $$M_{m,n}$$ if the characteristic of K is 0 or, more general, if the orbit map is separable. In positive characteristic however, the problem is more subtle since the orbit map is in general not separable, as we show by an example. This fact had been overlooked in previous papers. Our main result is a general sufficient criterion for finite G-determinacy in $$M_{m,n}$$ in arbitrary characteristic in terms of the tangent image of the orbit map, which we introduce in this paper. This criterion provides a computable bound for the G-determinacy of a matrix A in $$M_{m,n}$$ , which is new even in characteristic 0.

Orientation-dependent imaging of electronically excited quantum dots.

We previously demonstrated that we can image electronic excitations of quantum dots by single-molecule absorption scanning tunneling microscopy (SMA-STM). With this technique, a modulated laser beam periodically saturates an electronic transition of a single nanoparticle, and the resulting tunneling current modulation ΔI(x0, y0) maps out the SMA-STM image. In this paper, we first derive the basic theory to calculate ΔI(x0, y0) in the one-electron approximation. For near-resonant tunneling through an empty orbital "i" of the nanostructure, the SMA-STM signal is approximately proportional to the electron density φix0,y02 of the excited orbital in the tunneling region. Thus, the SMA-STM signal is approximated by an orbital density map (ODM) of the resonantly excited orbital at energy Ei. The situation is more complex for correlated electron motion, but either way a slice through the excited electronic state structure in the tunneling region is imaged. We then show experimentally that we can nudge quantum dots on the surface and roll them, thus imaging excited state electronic structure of a single quantum dot at different orientations. We use density functional theory to model ODMs at various orientations, for qualitative comparison with the SMA-STM experiment. The model demonstrates that our experimentally observed signal monitors excited states, localized by defects near the surface of an individual quantum dot. The sub-nanometer super-resolution imaging technique demonstrated here could become useful for mapping out the three-dimensional structure of excited states localized by defects within nanomaterials.

Numerical Bifurcation Analysis of Homoclinic Orbits Embedded in One-Dimensional Manifolds of Maps

We describe new methods for initializing the computation of homoclinic orbits for maps in a state space with arbitrary dimension and for detecting their bifurcations. The initialization methods build on known and improved methods for computing one-dimensional stable and unstable manifolds. The methods are implemented in M at C ont M, a freely available toolbox in Matlab for numerical analysis of bifurcations of fixed points, periodic orbits, and connecting orbits of smooth nonlinear maps. The bifurcation analysis of homoclinic connections under variation of one parameter is based on continuation methods and allows us to detect all known codimension 1 and 2 bifurcations in three-dimensional (3D) maps, including tangencies and generalized tangencies. M at C ont M provides a graphical user interface, enabling interactive control for all computations. As the prime new feature, we discuss an algorithm for initializing connecting orbits in the important special case where either the stable or unstable manifold is one-dimensional, allowing us to compute all homoclinic orbits to saddle points in 3D maps. We illustrate this algorithm in the study of the adaptive control map, a 3D map introduced in 1991 by Frouzakis, Adomaitis, and Kevrekidis, to obtain a rather complete bifurcation diagram of the resonance horn in a 1:5 Neimark-Sacker bifurcation point, revealing new features.

Moving average network examples for asymptotically stable periodic orbits of monotone maps

Moving average network examples for asymptotically stable periodic orbits of monotone maps

Basic feature quantities for analysis of periodic orbits in digital return maps

Basic feature quantities for analysis of periodic orbits in digital return maps

Convergence of inexact orbits of monotone nonexpansive mappings

We study monotone nonexpansive self-mappings of a closed and convex cone in an ordered Banach space with particular emphasis on the asymptotic behavior of their inexact iterates.

Folded symplectic toric four-manifolds

We show that two orientable, four-dimensional folded symplectic toric manifolds are isomorphic provided that their orbit spaces have trivial degree-two integral cohomology and there exists a diffeomorphism of the orbit spaces (as manifolds with corners) preserving orbital moment maps.

Pentavalent phosphorus as a unique phosphorus donor in POCl3 homodimer and POCl3-H2O heterodimer: matrix isolation infrared spectroscopic and computational studies.

Phosphorus, an important element among the pnicogen group, opens up avenues for experimental and computational explorations of its interaction in a variety of compounds. Although experimental proof of trivalent phosphorus bonding is limited and is growing with time, phosphorus bonding with pentavalent phosphorus has been a long sought after interaction both computationally and experimentally. In the present work, for the first time, we have provided unambiguous experimental evidence for the pentavalent phosphorus bonding interaction by exploiting a phosphoryl chloride (POCl3) prototype under isolated conditions at low temperatures. The POCl3 dimer and higher aggregates can be set as a unique example possessing pentavalent phosphorus bonding with a competing halogen bonding interaction. The POCl3-H2O heterodimer is another interesting system, stabilized through multiple phosphorus and hydrogen bonded interactions. Using matrix isolation infrared spectroscopy, the POCl3 homodimer and POCl3-H2O heterodimer were characterized and the structures were elucidated by employing ab initio and DFT methods. The multifaceted interactions in the POCl3 paradigm were investigated by using Natural Bond Orbital, Energy Decomposition and Electrostatic Potential Mapping analyses.

Finite orbits in multivalued maps and Bernoulli convolutions

Bernoulli convolutions are certain measures on the unit interval depending on a parameter β between 1 and 2. In spite of their simple definition, they are not yet well understood. We study their two-dimensional density which exists by a theorem of Solomyak. To each Bernoulli convolution, there is an interval D called the overlap region, and a map which assigns two values to each point of D and one value to all other points of [0,1]. There are two types of finite orbits of these multivalued maps which correspond to zeros and potential singularities of the density, respectively.Orbits which do not meet D belong to an ordinary map called β-transformation and exist for all β>1.6182. They were studied by Erdös, Jóo, Komornik, Sidorov, de Vries and others as points with unique addresses, and by Jordan, Shmerkin and Solomyak as points with maximal local dimension. In the two-dimensional view, these orbits form address curves related to the Milnor–Thurston itineraries in one-dimensional dynamics. The curves depend smoothly on the parameter and represent quantiles of all corresponding Bernoulli convolutions.Finite orbits which intersect D have a network-like structure and can exist only at Perron parameters β. Their points are intersections of extended address curves, and can have finite or countable number of addresses, as found by Sidorov. For an uncountable number of parameters, the central point 12 has only two addresses. The intersection of periodic address curves can lead to singularities of the measures. We give examples which are not Pisot or Salem parameters.

Dipicolinate salt of imidazole: Discovering its structure and properties using different experimental methodologies and quantum chemical investigations

A novel organic proton transfer complex of imidazolium dipicolinate (ID) has been synthesized and it was grown as single crystals using slow evaporation method. The molecular structure of synthesized compound and vibrational modes of its functional groups were confirmed by (1H and 13C) NMR, FTIR and FT-Raman spectroscopic studies, respectively. Single crystal X-ray diffraction (SCXRD) analysis confirmed the orthorhombic system with noncentrosymmetric (NCS), P212121, space group of grown ID crystal. UV–Vis–NIR spectral study confirmed its high optical transparency within the region of 285–1500 nm. Powder second harmonic generation (SHG) efficiency of ID crystal was confirmed and it was 6.8 times that of KDP crystal. TG-DTA and DSC analysis revealed the higher thermal stability of grown crystal as 249 °C. The dielectric response and mechanical behaviour of grown crystal were studied effectively. Density functional theory calculations were performed to probe the relationship between the structure and its properties including molecular optimization, Mulliken atomic charge distribution, frontier molecular orbital (FMOs) and molecular electrostatic potential map (MEP) analysis and first hyperpolarizability. All these experimental and computational results were discussed in this communication and it endorsed the ID compound as a potential NLO candidate could be employed in optoelectronics device applications in near future.

Hyperbolic extensions of free groups

Given a finitely generated subgroup $\Gamma \le \mathrm{Out}(\mathbb{F})$ of the outer automorphism group of the rank $r$ free group $\mathbb{F} = F_r$, there is a corresponding free group extension $1 \to \mathbb{F} \to E_{\Gamma} \to \Gamma \to 1$. We give sufficient conditions for when the extension $E_{\Gamma}$ is hyperbolic. In particular, we show that if all infinite order elements of $\Gamma$ are atoroidal and the action of $\Gamma$ on the free factor complex of $\mathbb{F}$ has a quasi-isometric orbit map, then $E_{\Gamma}$ is hyperbolic. As an application, we produce examples of hyperbolic $\mathbb{F}$-extensions $E_{\Gamma}$ for which $\Gamma$ has torsion and is not virtually cyclic. The proof of our main theorem involves a detailed study of quasigeodesics in Outer space that make progress in the free factor complex. This may be of independent interest.

The Ac-5 (Fejokoo) quadrangle of Ceres: Geologic map and geomorphological evidence for ground ice mediated surface processes

NASA's Dawn spacecraft arrived at Ceres on March 6, 2015, and has been studying the dwarf planet through a series of successively lower orbits. Throughout these mission phases Dawn obtained photographic, mineralogical, elemental abundance, and gravity data. Ceres is the largest object in the asteroid belt with a mean diameter of ∼940 km. The Dawn Science Team conducted a geologic mapping campaign for Ceres similar to the one that was implemented on the asteroid Vesta (Dawn's previous target), including production of a Survey- and High Altitude Mapping Orbit (HAMO)-based global map, and a series of 15 Low Altitude Mapping Orbit (LAMO)-based quadrangle maps. In this paper we present the LAMO-based geologic map of the Ac-5 Fejokoo Quadrangle (21–66°N and 270–360°E) and discuss its implications. The Ac-5 quadrangle is primarily composed of ancient cratered terrain punctuated with several moderately fresh impact craters of geologic interest, six large tholi that are possibly cryovolcanic in origin, and an abundance of flows that well represent the full spectrum of mass wasting features observed on Ceres. The Fejokoo quadrangle hosts the majority of Oxo crater, the site of the first spectroscopic detection of H2O ice on the surface of Ceres. The H2O detection is closely related to two distinctive morphological units interpreted as possible high water ice content landslides. These observations and interpretations are consistent with ground ice mediated surface processes on Ceres.

Should Virtual Mirroring Be Used in the Preoperative Planning of an Orbital Reconstruction?

Mirroring has been used as a diagnostic tool in orbital wall fractures for many years, but limited research is available proving the assumed symmetry of orbits. The purpose of this study was to evaluate volume and contour differences between orbital cavities in healthy humans. In this cross-sectional study, the left and right orbital cavities of a consecutive sample of patients' computed tomograms were measured. Inclusion criteria were patients with no sign of orbital or sinus pathology or fracture. Outcome variables were differences in volume and contour. Descriptive statistics and Student paired t test were used for data analysis of orbital volume and distance maps were used for analysis of orbital contour. The sample was composed of 100 patients with a mean age of 57; 50% were men. The total mean orbital volume was 27.53±3.11mL. Mean difference between cavities was 0.44±0.31mL or 1.59% (standard deviation [SD], 1.10%). The orbital contour showed high similarity, with an absolute mean left-versus-right difference of 0.82mm (SD, 0.23mm). The authors hypothesize that the measured differences between right and left orbital volumes and contours are clinically minor. In consequence, the use of mirroring tools as part of preoperative planning in orbital reconstruction is legitimate with the aim of simulating the pre-traumatized anatomy.

Mapping stable direct and retrograde orbits around the triple system of asteroids (45) Eugenia

It is widely accepted that knowing the composition and the orbital evolution of asteroids might help us to understand the process of formation of the Solar system. It is also known that asteroids can represent a threat to our planet. Such an important role has made space missions to asteroids a very popular topic in current astrodynamics and astronomy studies. Taking into account the increasing interest in space missions to asteroids, especially to multiple systems, we present a study that aims to characterize the stable and unstable regions around the triple system of asteroids (45) Eugenia. The goal is to characterize the unstable and stable regions of this system and to make a comparison with the system 2001 SN263, which is the target of the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) mission. A new concept was used for mapping orbits, by considering the disturbance received by the spacecraft from all perturbing forces individually. This method has also been applied to (45) Eugenia. We present the stable and unstable regions for particles with relative inclination between 0° and 180°. We found that (45) Eugenia presents larger stable regions for both prograde and retrograde cases. This is mainly because the satellites of this system are small when compared to the primary body, and because they are not close to each other. We also present a comparison between these two triple systems, and we discuss how these results can guide us in the planning of future missions.

The unique geomorphology and structural geology of the Haulani crater of dwarf planet Ceres as revealed by geological mapping of equatorial quadrangle Ac-6 Haulani

The dwarf planet Ceres has been explored by NASA's Dawn spacecraft with the goal of characterizing its geology, mineralogy, topography, shape, and internal structure. One outcome of this exploration is the production of geologic maps, meant to unveil the geologic history of Ceres. In this paper, we present the geologic map of the Ac-6 Haulani quadrangle (Lat. 22°S-22°N, Long. 0°–72°E) based on Low Altitude Mapping Orbit (LAMO) (∼35 m/pixel) data supplemented with color and spectral data, as well as a digital terrain model from the High Altitude Mapping Orbit (HAMO) (∼135 m/pixel, vertical accuracy of about 10 m). The 34 km diameter Haulani crater is one of the youngest features on Ceres and the most prominent one in the quadrangle. Haulani was formed on a topographical transition in north–south direction and shows a complex morphology with a variety of lobate flows and tectonic features. Multiple cracks and depressions around the crater indicate the failure of subsurface material. These were likely formed by the subsidence of material due to the instability of the subsurface. The mapping of Ac-6 Haulani suggests that Ceres is built up of layers with different material properties. We propose that Ceres has a solid crust and a variable ice-rich subsurface consistent with previous and recent models of Ceres' interior.