One-sided invertibility of discrete operators and their applications

For \(p\in [1,\infty ]\), we establish criteria for the one-sided invertibility of binomial discrete difference operators \({{\mathcal {A}}}=aI-bV\) on the space \(l^p=l^p(\mathbb {Z})\), where \(a,b\in l^\infty \), I is the identity operator and the isometric shift operator V is given on functions \(f\in l^p\) by \((Vf)(n)=f(n+1)\) for all \(n\in \mathbb {Z}\). Applying these criteria, we obtain criteria for the one-sided invertibility of binomial functional operators \(A=aI-bU_\alpha \) on the Lebesgue space \(L^p(\mathbb {R}_+)\) for every \(p\in [1,\infty ]\), where \(a,b\in L^\infty (\mathbb {R}_+)\), \(\alpha \) is an orientation-preserving bi-Lipschitz homeomorphism of \([0,+\infty ]\) onto itself with only two fixed points 0 and \(\infty \), and \(U_\alpha \) is the isometric weighted shift operator on \(L^p(\mathbb {R}_+)\) given by \(U_\alpha f= (\alpha ^\prime )^{1/p}(f\circ \alpha )\). Applications of binomial discrete operators to interpolation theory are given.     

Investigations of shock wave interaction with nanosecond surface discharge

Non-stationary plane shock wave interaction with localized nanosecond-lasting surface discharges was investigated. Pulse discharge plasma glow evolution was recorded with a CCD camera and gas flow evolution was recorded with laser shadowgraphy. CFD simulations of pulse energy deposition near the horizontal wall surface in front of the shock wave were carried out. Non-stationary 2D symmetrical flow dynamics were studied and analysis of the instantaneous surface discharge energy rate through CFD and shadow images matching was carried out.     

The Morpho-Functional Characteristics of Cerebral and Renal Arteries After Induced Arterial Hypertension in Rats Using Magnetic Resonance Imaging

The morpho-functional reorganization of regional vascular arteries is greatly altered after the induction of arterial hypertension (AH) in experimental rats. These changes can be examined using magnetic resonance imaging methods. In our experiment, induced AH caused arteriostenosis of cerebral arteries in two strains of rats—Wistar and OXYS (p < 0.05). In addition, we studied the changes in renal arteries in the same experiment. Compensatory vasodilatation was found in the extrarenal part of arteries. Arteriostenosis was detected in the intrarenal part of arteries, which was due to cytotoxic hypostasis of renal parenchyma. We proposed a cerebral vascular index and applied this index for precise analysis of changes in the studied arteries. This index is calculated as the ratio of the diameter of cerebral arteries to the diameter of renal arteries. The degree of differences in vasoconstriction between cerebral and renal arteries was established. Our results showed a moderate degree of differences in the vasoconstriction of cerebral arteries. In addition, the degree of differences in the vasoconstriction of intrarenal arteries revealed deeper vasoconstriction. These distinctions are 28.1% (p < 0.05) and 60.9% (p < 0.05) for Wistar and OXYS rats, respectively. Arterial morphometry revealed reduced sizes of all OXYS rat arteries compared with those of Wistar rat arteries. These pathological changes were associated with excessive stiffness (rigidity) of vascular walls due to accelerated aging. The accelerated aging of OXYS rat arteries led to a decrease in their vasodilatation potential and a decrease in the blood supply of cerebral and renal arteries. Comparative morphometry of the status of all arteries in both groups after AH revealed multiple specific changes in the remodeled arteries.     

Formation of self-assembled monolayers of alkylphosphonic acid on the native oxide surface of SS316L

Phosphonate-steel interactions have been industrially significant for decades, but details of the phosphonate-steel interface have not yet been characterized. Self-assembled monolayers of phosphonic acids were formed on stainless steel 316L by room-temperature solution deposition. The acids are covalently bound to the surface as phosphonates in a bidentate manner, as determined by diffuse reflectance Fourier transform infrared spectroscopy and X-ray photoelectron spectroscopy. Complete coverage of the surface is confirmed by contact angle measurement and atomic force microscopic imaging. This method of monolayer formation contrasts the requirement for heating and long reaction times found to be necessary to form phosphonate monolayers on other metal oxide substrates, such as titanium and silicon.     

Diffusion-induced Ramsey narrowing

Diffusion-induced Ramsey narrowing is characterized and identified as a general phenomenon, in which diffusion of coherence in and out of an interaction region such as a laser beam induces spectral narrowing of the associated resonance line shape. Illustrative experiments and an intuitive analytical model are presented for this spectral narrowing effect, which occurs commonly in optically interrogated atomic systems and may also be relevant to quantum dots and other solid-state spin systems.     

Cancellation of light shifts in an N-resonance clock

We demonstrate that first-order light shifts can be canceled for an all-optical, three-photon-absorption resonance (N-resonance) on the D1 transition of 87Rb. This light-shift cancellation facilitates improved frequency stability for an N-resonance clock. For example, by using a tabletop apparatus designed for N-resonance spectroscopy, we measured a short-term fractional frequency stability (Allan deviation) of approximately/= 1.5 x 10(-11) tao1/2 for observation times of 1 s < or = tao < or = 50 s. Further improvements in frequency stability should be possible with an apparatus designed as a dedicated N-resonance clock.     

A simulation study of the fleet sizing problem arising in offshore anchor handling operations

A fleet sizing problem arising in anchor handling operations related to movement of offshore mobile units is presented in this paper. Typically, the intensity of these operations is unevenly spread throughout the year. The operations are performed by dedicated vessels, which can be hired either on the long-term basis or on the spot market. Spot rates are frequently a magnitude higher than long-term rates, and vessels are hired on the spot market if there is a shortage of long-term vessels to cover the ongoing anchor handling operations. Deciding the cost-optimal fleet of vessels on the long-term hire to cover future operations is a problem facing offshore oil and gas operators. This decision has a heavy economic impact as anchor handling vessels are among the most expensive ones. The problem is highly stochastic because durations of anchor handling operations vary and depend on uncertain weather conditions. Moreover, future spot rates for anchor handling vessels are extremely volatile. The objective of this paper is to describe a simulation model for the fleet sizing problem. The study was initiated by the largest Norwegian offshore oil and gas operator and has received considerable acceptance among the planners.     

Corrosion properties of nickel coatings obtained from aqueous and nonaqueous electrolytes

Nickel was deposited on a copper substrate from aqueous and nonaqueous ethanol electrolytes. X-ray photoelectron spectroscopy, electrochemical impedance spectroscopy and chronovoltametry, scanning electron microscopy, and atomic force microscopy were used to study the effect of the solvent on the surface and corrosion properties of the Ni coatings formed. Unifom and relatively smooth Ni films were obtained as measured with microscopy techniques. The formation of a passive film in acidic, alkaline, and neutral chloride-containing media was confirmed with X-ray photoelectron spectroscopy. The water-based nickel-plating electrolyte makes it possible to deposit coatings with higher corrosion resistance as compared with coatings deposited from ethanol electrolyte in NaOH and NaCl media. The proposed mechanism of corrosion in a 0.5 M H₂SO₄ solution involves cycles of active-passive surface behavior due to its passivation by corrosion products.     

Polymorphism of 3‐(5‐phenyl‐1,3,4‐oxadiazol‐2‐yl)‐ and 3‐[5‐(pyridin‐4‐yl)‐1,3,4‐oxadiazol‐2‐yl]‐2H‐chromen‐2‐ones

This study of 3‐(5‐phenyl‐1,3,4‐oxadiazol‐2‐yl)‐2H‐chromen‐2‐one, C₁₇H₁₀N₂O₃, 1 , and 3‐[5‐(pyridin‐4‐yl)‐1,3,4‐oxadiazol‐2‐yl]‐2H‐chromen‐2‐one, C₁₆H₉N₃O₃, 2 , was performed on the assumption of the potential anticancer activity of the compounds. Three polymorphic structures for 1 and two polymorphic structures for 2 have been studied thoroughly. The strongest intermolecular interaction is stacking of the `head‐to‐head' type in all the studied crystals. The polymorphic structures of 1 differ with respect to the intermolecular interactions between stacked columns. Two of the polymorphs have a columnar or double columnar type of crystal organization, while the third polymorphic structure can be classified as columnar‐layered. The difference between the two structures of 2 is less pronounced. Both crystals can be considered as having very similar arrangements of neighbouring columns. The formation of polymorphic modifications is caused by a subtle balance of very weak intermolecular interactions and packing differences can be identified only using an analysis based on a study of the pairwise interaction energies.