Adjacent Corners Research Articles

Scale-Space Behavior of Planar-Curve Corners

The curvature scale-space (CSS) technique is suitable for extracting curvature features from objects with noisy boundaries. To detect corner points in a multiscale framework, Rattarangsi and Chin investigated the scale-space behavior of planar-curve corners. Unfortunately, their investigation was based on an incorrect assumption, viz., that planar curves have no shrinkage under evolution. In the present paper, this mistake is corrected. First, it is demonstrated that a planar curve may shrink nonuniformly as it evolves across increasing scales. Then, by taking into account the shrinkage effect of evolved curves, the CSS trajectory maps of various corner models are investigated and their properties are summarized. The scale-space trajectory of a corner may either persist, vanish, merge with a neighboring trajectory, or split into several trajectories. The scale-space trajectories of adjacent corners may attract each other when the corners have the same concavity, or repel each other when the corners have opposite concavities. Finally, we present a standard curvature measure for computing the CSS maps of digital curves, with which it is shown that planar-curve corners have consistent scale-space behavior in the digital case as in the continuous case.

2J Si−O−Si Scalar Spin−Spin Coupling in the Solid State: Crystalline and Glassy Wollastonite CaSiO3

We have investigated the 29Si−O−29Si 2J scalar spin−spin coupling constant in two crystalline polymorphs and in a glass of 29Si isotopically enriched wollastonite CaSiO3 composition. In the crystalline samples, line widths of less than 1 Hz are observed in the indirect dimension of a simple J-resolved NMR experiment leading to 2JSiOSi values of 1.5, 3.6, and 8.0 Hz determined with a high accuracy of ±0.1 Hz. The very high resolution obtained with those two compositions enabled us to evidence strong coupling effects in the J-resolved two-dimensional spectra. In particular, additional lines in J-spectra are seen here for the first time in solid-state NMR experiments of inorganic samples. Cluster ab initio calculations led us to propose a stereochemical analysis of 2J, leading to a close-to-linear relationship between 2JSiOSi and the Si−O−Si bonding angle Ω ≃ 3.41J + 127 which takes into account the predominant influence of the Ca atoms. In the glass, this relationship allowed the analysis of the distribution of angle within each Q(n) species. The classical relationship between the 29Si isotropic chemical shift and the average Si−O−Si bond angle is experimentally confirmed and quantified. The most probable set of Ω’s are 128.0° for Q(1), (131.8°,135.4°) for Q(2), and (132.5°,137.1°,144.3°) for Q(3), and the presence of three-membered rings is evidenced. An unexpectedly strong correlation between the bonding at each corner of a given Q(n) unit and the bonding at adjacent corners is found.

Magnetostatic dipolar domain-wall pinning in chains of permalloy triangular rings

In a combined experimental and numerical study, we investigated the details of the motion and pinning of domain walls in isolated and interacting permalloy triangular rings (side $2\text{ }\ensuremath{\mu}\text{m}$, width 250 nm, and thickness 25 nm). To induce interaction between the rings, they were arranged either in vertical chains with an apex of each triangle in proximity to the edge center of the triangle above it or in horizontal chains where the proximity is between the adjacent corners of the triangles. Using longitudinal and diffraction magneto-optic Kerr effects, magnetic force microscopy, and micromagnetic simulations, we determined the field dependence of the spin structure in the rings. In all cases the remnant state of each ring is an ``onion'' state characterized by two domain walls---one head to head the other tail to tail---pinned at the apexes. In isolated rings the magnetization reversal occurs between two onion states via the formation of an intermediate vortex state, which arises from the motion and annihilation of the two domain walls. In the case of the horizontal chains the reversal mechanism is unchanged except that the dipolar interaction affects the field range in which the rings are in the vortex state. In the case of vertical chains an additional intermediate state is observed during reversal. The new state involves a domain wall pinned at the center of the edge that is in close proximity to the apex of its neighbor. We show that the domain-wall motion in this last case can be modeled by a triple potential well. Because the new state requires that a domain wall be pinned at the neighboring apex, our observations can be viewed as a very elementary form of magnetic logic.

Translational Joints With Clearance in Rigid Multibody Systems

A computational methodology for dynamic description of rigid multibody systems with translational clearance joints is presented and discussed in this work. Over the past years, extensive work has been done to study the dynamic effect of the revolute joints with clearance in multibody systems, in contrast with the little work devoted to model translational joints with clearance. In a joint with translation clearance, there are many possible ways to set the physical configuration between the slider and guide, namely: (i) no contact between the two elements, (ii) one corner of the slider in contact with the guide surface, (iii) two adjacent slider corners in contact with the guide surface, and (iv) two opposite slider corners in contact with the guide surfaces. The proposed methodology takes into account these four different situations. The conditions for switching from one case to another depend on the system dynamics configuration. The existence of a clearance in a translational joint removes two kinematic constraints from a planar system and introduces two extra degrees of freedom in the system. Thus, a translational clearance joint does not constrain any degree of freedom of the mechanical system but it imposes some restrictions on the slider motion inside the guide limits. When the slider reaches the guide surfaces, an impact occurs and the dynamic response of the joint is modeled by contact-impact forces. These forces are evaluated here with continuous contact force law together with a dissipative friction force model. The contact-impact forces are introduced into the system’s equations of motion as external generalized forces. The proposed methodology is applied to a planar multibody mechanical system with a translational clearance joint in order to demonstrate its features.

A derivation of the van der Pauw formula from electrostatics

The van der Pauw formula for determining the electrical resistivity of an irregularly-shaped material was derived by him with the help of conformal mapping and is inherently two-dimensional. Thus, it is valid in the limiting case of a sample of infinitesimal thickness. In this paper, we demonstrate how the same formula can be derived from classical electrostatics for a rectangular sample of non-zero thickness which is allowed to approach zero. The calculation is carried out with the current probes at two adjacent corners and the voltage probes at the other two. In addition, the effects of non-ideality, particularly non-zero thickness and non-point contact voltage and current probes, are examined using the analytic formulation derived here and a semiconductor device code.

A novel solution for pressure drop in singly connected microchannels of arbitrary cross-section

This paper outlines a novel approximate solution for determining the pressure drop of fully developed, laminar, single-phase flow in singly connected microchannels of arbitrary cross-section. Using a “bottom-up” approach, it is shown that for constant fluid properties and flow rate in fixed cross-section channels, the Poiseuille number is only a function of geometrical parameters of the cross-section, i.e., perimeter, area, and polar moment of inertia. The proposed model is validated with experimental data for rectangular, trapezoidal, and triangular microchannels. The model is also compared against numerical results for a wide variety of channel cross-sections including: hyperellipse, trapezoid, sine, square duct with two adjacent round corners, rhombic, circular sector, circular segment, annular sector, rectangular with semi-circular ends, and moon-shaped channels. The model predicts the pressure drop for the cross-sections listed within 8% of the values published.

1-Methyl-4-(methylamino)piperidine-platinum(II) adducts with DNA bases

A series of platinum(II) monoadducts and diadducts of the type [PtII(mmap)LCl]NO3 and [PtII(mmap)L2](NO3)2 (where mmap = 1-methyl-4-(methylamino)piperidine and L = adenine, 9-methylguanine, 7-methylguanine, cytosine, or uracil) have been synthesized and characterized by elemental analyses and by 1H, 13C, and 195Pt nuclear magnetic resonance spectroscopy. Two adjacent corners of the platinum plane were occupied by the two amino nitrogens of 1-methyl-4-(methylamino)piperidine and the other two positions were occupied by the chloride and nitrogen atoms of the DNA base in monoadducts and two nitrogen atoms of DNA bases in diadducts.

Scanning tunnelling microscopy study of atomic hydrogen adsorption on the Si(111) 7 × 7 surface

We studied initial atomic hydrogen adsorption onto Si(111) 7 × 7 adatoms by scanning tunnelling microscopy in an ultrahigh vacuum. Adatom reaction probabilities were measured as a function of atomic hydrogen exposure time for room-temperature and hightemperature surfaces. Hydrogen uptake was well represented by Langmuir adsorption at 361 and 414 K, while depression of uptake was seen at 481 K after one of six adatoms was terminated by hydrogen. Hydrogen adsorption had positive adsorption correlations between adjacent centre adatoms and corner adatoms across the 7 × 7 half unit. These correlations were enhanced at 481 K. In accordance with the positive reaction correlation between these adjacent adatoms, the average number of reacted adatoms in adjacent 7 × 7 half units was also enhanced as the number of reacted adatoms increased in the half unit.

SAPHO Syndrome: MR Appearance of Vertebral Involvement

To retrospectively evaluate the magnetic resonance (MR) imaging findings of vertebral involvement in patients with synovitis, acne, pustulosis, hyperostosis, and osteitis (SAPHO) syndrome. Ethics committee approval and informed patient consent were not required for this retrospective study. MR images obtained in 12 patients (seven female, five male; mean age, 42 years; range, 16-65 years) with SAPHO syndrome involving the spine were reviewed. One vertebral lesion separated by one or more normal vertebrae was analyzed as a distinct lesion. For each lesion, the number of associated vertebrae with abnormal signal intensity (SI) (ie, single vertebra, two adjacent vertebrae, or more than two adjacent vertebrae) was noted. The following MR imaging findings were evaluated: cortical bone erosion, abnormal vertebral body SI compared with normal vertebral body SI, increased anteroposterior diameter of the vertebral body, soft-tissue involvement, vertebral body height loss of more than 30%, and abnormal SI of the adjacent intervertebral disk compared with the SI of the other disks. Of 24 vertebral lesions found, 17 involved a single vertebra, four involved two adjacent vertebrae, and three involved three or four adjacent vertebrae. Vertebral corner cortical erosion was present in all lesions, and 23 (96%) lesions had anterior vertebral corner involvement. The erosion was confined to a vertebral corner in five (21%) lesions and included the adjacent endplate and/or the anterior cortex of the vertebral body in the remaining 19 (79%) lesions. In four (17%) lesions, involvement of two adjacent vertebral corners on either side of an intervertebral disk mimicked to some extent early disk space infection. An adjacent disk space was narrowed in six (25%) lesions and exhibited abnormal SI in two (8%). Prevertebral tissue thickening was observed in eight (33%) lesions. Erosion of a vertebral body corner is consistently seen on MR images of SAPHO vertebral lesions and may support the diagnosis of SAPHO syndrome in the appropriate clinical context.

X-ray structure and multinuclear NMR studies of platinum(II) complexes with 5-methyl-1,2,4-triazolo[1,5- a]pyrimidin-7(4 H)-one

New dichloride platinum(II) complexes with 5-methyl-1,2,4-triazolo[1,5- a]pyrimidin-7(4 H)-one (HmtpO) have been synthesized and characterized by thermal analysis, infrared and 1H, 13C, 15N, 195Pt NMR spectroscopy. X-ray crystal structures of cis-PtCl 2(NH 3)(HmtpO) ( 1) and cis-PtCl 2(HmtpO) 2 · 4H 2O ( 2b) were determined to R = 0.0332 and R = 0.0802, respectively. In both complexes the Pt(II) ions have a square-planar geometry with two adjacent corners being occupied by two nitrogens of HmtpO molecules for 2b or NH 3 and HmtpO molecules for 1, whereas the remaining adjacent corners are occupied by two chloride anions. Spectroscopic data confirm the square planar geometry with N(3) bonded HmtpO, S-bonded dimethylsulfoxide and two trans chloride anions for trans-PtCl 2(dmso) · 4H 2O ( 3).

Synthesis characterization and X-ray crystal structures of cis-1,4-diaminocyclohexane-platinum(II) nucleobase adducts

Platinum complexes of the type [Pt( cis-1,4-DACH)(L) 2]X, where cis-1,4-DACH = cis-1,4-diaminocyclohexane; L = adenine (ade) ( 1), hypoxanthine (hyp) ( 2), 9-methylguanine (9-megua) ( 3), cytosine (cyt) ( 4), or 1-methylcytosine (1-mecyt) ( 5); and X = SO 4 or Cl 2 groups, were synthesized and characterized by elemental analysis and by 1H, 13C, and 195Pt nuclear magnetic resonance spectroscopy. The crystals of [Pt( cis-1,4-DACH)(9-megua) 2]SO 4[9-megua-H] 2SO 4 ( 3) and [Pt( cis-1,4-DACH)(1-mecyt) 2]Cl 2 · 6H 2O ( 5) were also subjected to single-crystal X-ray diffraction. The base/PtN4 coordination plane dihedral angles were 74.55° and 85.61° in complex 3 and 78.12° and 81.80° in complex 5. The platinum had distorted square planar geometry in both complexes; the two adjacent corners were occupied by the two nitrogen atoms of cis-1,4-DACH, and the other two corners were occupied by the two N7 atoms of 9-megua in complex 3 and the two N3 atoms of 1-mecyt in complex 5. The cis-1,4-DACH, which has a unique twist-boat configuration, formed a seven-member chelating ring with platinum, which led to considerable strain during bidentate cis-1,4-DACH binding. Cations of both complexes 3 and 5 adopted C 2 molecular symmetry. These adducts were the models for the intrastand cross-links that were relevant to the binding of the Pt(II) antitumor drugs to DNA.

Scanning tunneling microscopy study on initial stage of atomic hydrogen adsorption on the Si(1 1 1) 7 × 7 surface

Initial hydrogen adsorption on the Si(1 1 1) 7 × 7 surface was studied by scanning tunneling microscopy (STM) in an ultrahigh vacuum. Room temperature adsorbed hydrogen on the adatom in the 7 × 7 reconstruction led to depression of adatoms in the STM images. The hydrogen uptake curve at the adatom site as a function of hydrogen exposure time was well represented by Langmuir adsorption. No preferential adsorption was seen among four inequivalent adatoms in the 7 × 7 reconstruction. Adsorption of the adjacent center and corner adatoms respectively showed ∼10% higher adsorption. Even though the number of reacted adatoms in the half unit of the 7 × 7 reconstruction was statistically random, the number of reacted adatoms in the nearest neighbor half unit was enhanced as the number of reacted sites increased in the half unit.

Eddy-current analysis of a conductor with a crack by line integral equations with loop electric and magnetic currents as unknowns

It is difficult to calculate eddy currents induced in a conductor with a crack by the surface integral equations because its adjacent edges and corners, where the equations become singular, are close, and moreover, the equations become ill-conditioned in cases where the crack gap is narrow. In this paper, we propose a method employing line integral equations with loop electric and magnetic currents as unknowns fully utilizing the boundary conditions of the surface electromagnetic fields. Solving eddy-current problems and comparing the results with those by FEM, we study how to calculate accurately the eddy currents induced in a conductor with a crack

Homopiperazine Pt(II) adducts with DNA bases and nucleosides: Crystal structure of [Pt II(homopiperazine)(9-ethylguanine) 2](NO 3) 2

A series of platinum(II) mono- and diadducts of the type [Pt II(hmp)XCl]NO 3 and [Pt II(hmp)X 2](NO 3) 2 (where hmp = homopiperazine and X = adenine, 9-ethylguanine, 7-methylguaninine, cytosine, 1-methylcytosine, or cytidine), have been synthesized and characterized by elemental analysis and by 1H, 13C, and 195Pt nuclear magnetic resonance spectroscopy. The crystal structure of diadduct [Pt II(homopiperazine)(9-ethylguanine) 2](NO 3) 2 was determined using a single crystal X-ray diffraction method. In this complex, platinum had a slightly distorted square planar geometry owing to the presence of a geometrically strained 5-membered ring. The two adjacent corners of the platinum plane were occupied by the two amino nitrogens of hmp, whereas the other two equatorial positions were occupied by two nitrogen atoms of two 9-ethylguanine. The 9-ethylguanine ligands are oriented in a head to tail fashion between 9-ethylguanine and platinum coordination plane possessing approximate C 2 molecular symmetry.

Bandwidth enhancement and size reduction of microstrip slot antennas

Reduced size microstrip monopole slot antennas with different slot shapes-straight, L and inverted T, and placed on a small ground plane, are investigated. The ground plane size is 50 mm/spl times/80 mm, which is about the size of a typical PC Wireless card. Detailed simulation and experimental investigations are conducted to understand their behavior and optimize for broadband operation. It is shown that, the variation in the slot shape, from straight to L and T shapes, helps in generating additional resonances, which when coupled to the original resonances of the slot, further increases impedance bandwidths. The bent shapes of the L and T slots reduce their height and provide more space on the ground plane for electronics. A mirror image dual L-slot antenna, placed at two adjacent corners of the ground plane, is also investigated and optimized for the polarization diversity. They provide an impedance bandwidth of 87%, with near orthogonal radiation characteristics. The measured impedance bandwidths (S/sub 11/=-10 dB) of up to 60%, 84%, and 80% are achieved for these straight, L and inverted T slots respectively, by suitably selecting their design parameters. The simulation results are in good agreement with the experimental data considering several practical issues.

Model platinum nucleobase and nucleoside complexes and antitumor activity: X-ray crystal structure of [Pt IV( trans-1 R,2 R-diaminocyclohexane) trans-(acetate) 2(9-ethylguanine)Cl]NO 3 · H 2O

A series of platinum(II) and (IV) monoadducts of the type [Pt II(DACH)LCl]NO 3 and [Pt IV(DACH) trans-(X) 2LCl]NO 3 (where DACH = trans-1 R,2 R-diaminocyclohexane, L = adenine, guanine, hypoxanthine, cytosine, adenosine, guanosine, inosine, cytidine, 9-ethylguanine (9-EtGua), or 1-methylcytosine and X = hydroxo or acetato ligand) have been synthesized and characterized by elemental analysis and by 1H and 195Pt nuclear magnetic resonance (NMR) spectroscopy. The crystal structure of the model nucleobase complex [Pt IV( trans-1 R,2 R-diaminocyclohexane) trans-(acetate) 2(9-EtGua)Cl]NO 3 · H 2O was determined using a single crystal X-ray diffraction method. The compound crystallized in the monoclinic space group P2 1, with a = 10.446(2) Å, b = 22.906(5) Å, c = 10.978(2) Å, Z = 4, and R = 0.0718, based upon the total of 11,724 collected reflections. In this complex, platinum had a slightly distorted octahedron geometry owing to the presence of a geometrically strained five-member ring. The two adjacent corners of the platinum plane were occupied by the two amino nitrogen of DACH, whereas, the other two equatorial positions occupied by chloride ion and 9-ethylguanine. The remaining two axial positions were occupied by the oxygen atoms of acetato ligands. The DACH ring was in a chair configuration. An intricate network of intermolecular hydrogen bonds held the crystal lattice together. Some of these synthesized models of DACH-Pt-DNA adducts have good in vitro cytotoxic activity against the cisplatin-sensitive human cancer ovarian A2780 cell line (IC50 = 1–8 μM). Interestingly, a substituted nucleobase (9-ethylguanine) adduct was over 6-fold more potent than regular adducts. The cross-resistance factor against the 44-fold cisplatin-resistant 2780CP/clone 16 cells was about 3–9; thus, the cytotoxicity of adducts was indicative of low potency, but the resistance factors were also substantially low. These results suggest that DNA adducts of DACH-Pt are cytotoxic with low cross-resistance.

Design of Stiffened Elements in Cold-Formed Stainless Steel Sections

The paper presents strength equations for single stainless steel stiffened elements applicable to the range of alloys included in the American, Australian, and European standards for stainless steel structures. Cold-formed sections with stiffened elements are considered and the enhanced mechanical properties of the corners are taken into account to show that the Winter equation may or may not conservatively predict the strength, depending on the corner area relative to the area of the flat part. The paper shows that the Winter equation may be used safely for the design of stiffened elements provided half of the area of the adjacent corners exceeds 10.15% of the flat area, depending on the alloy and whether the section is cold-rolled or brake-pressed. An equation is derived for determining the reduction factor to be applied to the Winter strength when the minimum corner area requirement is not met. The reduction factor is less than 10% for practical sections.

Preparation, characterization, and antitumor activity of new cisplatin analogues with 1-methyl-4-(methylamino)piperidine: Crystal structure of [Pt II(1-methyl-4-(methylamino) piperidine)(oxalate)

A series of new platinum(II) complexes of the type [Pt II(mmap)X] (where mmap, 1-methyl-4-(methylamino)piperidine and X, 1,1-cyclobutanedicarboxylato (CBDCA), oxalato, malonato, methylmalonato, dimethylmalonato, ethylmalonato, diethylmalonato or 2,3-naphthalene dicarboxylato (NDCA)) have been synthesized and characterized by elemental analysis, infrared (IR), and 13C and 195Pt nuclear magnetic resonance (NMR) spectroscopy. The crystal structure of the analogue [Pt II(mmap)(oxalate)] was determined using the single crystal X-ray diffraction method. Based upon a total of 4964 collected reflections, we determined that the compound crystallizes in the monoclinic space group P2 1/ c (with a=11.890(2) Å, b=9.6695(19) Å, c=9.875(2) Å, β=102.03(3)°, Z=4, and R=0.0428). In this complex, platinum has a slightly distorted square planar geometry with the two adjacent corners being occupied by two nitrogen atoms of the mmap ligand, whereas the remaining cis positions are occupied by two oxygen atoms of the oxalate molecule. The mmap ligand is in a boat conformation and forms six-membered chelating rings as well as the oxalate molecule forms five-membered chelating rings with platinum. The complexes were evaluated for their cytotoxic potential against the sensitive A2780 tumor model and cisplatin-resistant clone derived in vitro from potential cells.

An examination of small fatigue crack morphology

Test results for the growth of a small corner crack under cyclic loading are presented. The number of grains that are crossed by the crack front ranges from about three to ten during the crack advance. Crack path profile measurements on the adjacent corner faces are presented. Also, a microscopic examination of the crack path morphology of a polished and etched surface that is adjacent to the corner reveals the presence of complex branching mechanisms, and localized regions of intensive damage. Examination of sub-surfaces reveals that though branching and localized damage are present, they diminish with increasing depth of the subsurface. It is concluded that during early growth, the crack surface deviates substantially from an idealized planar surface model, and that Modes I, II, and III are all operative.

Synthesis and characterization of platinum(II) complexes with 3-methylpiperidine: crystal and molecular structure of [Pt(3-methylpiperidine) 2(malonato)]·H 2O

A series of new platinum complexes of the type [Pt(3-mepip) 2X] (where 3-mepip=3-methylpiperidine, and X=dichloro, sulfato, oxalato, malonato, methylmalonato, dimethylmalonato, tartronato, 1,1-cyclopropanedicarboxylato (CPDCA) or 1,1-cyclobutanedicarboxylato (CBDCA) ligand) were synthesized and characterized by elemental analysis, IR spectroscopy and 195Pt nuclear magnetic resonance spectroscopy. The crystal structure of [Pt(3-mepip) 2(malonato)]·0.79H 2O was determined by single crystal X-ray diffraction. In this complex platinum has slightly distorted square planar geometry with two adjacent corners being occupied by two nitrogens of 3-methylpiperidine, whereas the remaining two adjacent corners are occupied by two oxygen atoms of the malonato group. An intricate network of intermolecular hydrogen bonds holds the crystal lattice together. In the other complexes, 3-mepip acts as non-leaving ligands, whereas the carboxylato ligands act as leaving groups.