On strongly stable normal operators in Krein spaces

For bounded normal operators in Krein spaces we give a necessary and sufficient condition for strong stability. The same result for unitary operators was obtained by M.G.Krein [1] (see also [2]). For selfadjoint operators we refer to the papers of P.Jonas, H.Langer [3] and H.Langer [4].     

A touch of mathematics: coming to our senses by observing the visually impaired

During the last three decades, the impact of visualization processes on the teaching and learning of mathematics has been extensively researched. However, considerably less work has been devoted to haptic processes. In this paper, we describe and analyze the role of haptic processes from data collected in mathematics lessons taught in a school for blind students. The analysis builds upon studies from perception and also from teaching experiences in order to examine the teacher’s and the students’ hand movements and metaphors when handling solids of revolution and communicating verbally with each other about their insights. We highlight the powerful combination of the visual and the haptic components of their interactions for the conceptualization of mathematical experiences, and we also note the critical role mathematical language plays in supporting the teaching–learning processes in this context. Finally, we consider important educational implications not only for blind people, but for all students and teachers of mathematics.     

Gas permeability and selectivity of hexafluoroisopropylidene aromatic isophthalic copolyamides

The synthesis, thermal, and gas transport properties of poly(hexafluoroisopropylidene isophthalamide), HFA/ISO homopolymer, and HFA/TERT‐co‐HFA/ISO copolyamides with different poly(hexafluoroisopropilydene‐5‐t‐butylisophthalamide), HFA/TERT, ratios are reported. The results indicate that the glass transition temperatures of the copolyamides increase as the concentration of HFA/TERT in the polyamide increases. The gas permeability coefficients in the polyamides and copolyamides are independent of pressure or decrease slightly particularly with CO₂, N₂, and CH₄. It was seen that HFA/TERT is 2–6 times more permeable than HFA/ISO, depending on the gas being considered. This was assigned to the presence of the bulky lateral substituent, t‐butyl group in HFA/TERT and HFA/TERT‐co‐HFA/ISO copolyamides. This substituent increases fractional free‐volume, as expected. Therefore, the gas permeability and diffusion coefficients generally increase with increasing fractional free‐volume. The experimental results for the gas permeability and permselectivity for the copolyamides was well represented by a logarithmic mixing rule of the homopolyamides permeability coefficients and their volume fraction. The selectivity of gas pairs, such as O₂/N₂, CO₂/CH₄, and N₂/CH₄ decreased slightly with the addition of HFA/TERT. The temperature dependence of permeability for homopolyamides and copolyamides can be described by an Arrhenius type equation. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2625–2638, 2005     

Ultraheavy Yukawa-bound states of fourth-generation at Large Hadron Collider

A study of bound states of the fourth-generation quarks in the range of 500?C700 GeV is presented, where the binding energies are expected to be mainly of Yukawa origin, with QCD subdominant. Near degeneracy of their masses exhibits a new ??isospin??. The production of a colour-octet, isosinglet vector meson via $q\bar q \to \omega_8$ is the most interesting. Its leading decay modes are $\pi_8^\pm W^\mp$ , $\pi_8^0Z^0$ , and constituent quark decay, with $q\bar q$ and $t\bar t'$ and $b\bar b'$ subdominant. The colour octet, isovector pseudoscalar ?? ₈ meson decays via constituent quark decay, or to Wg. This work calls for more detailed study of fourth-generation phenomena at LHC.     

Gas permeability and selectivity of benzophenone aromatic isophthalic copolyamides

The synthesis, thermal, and gas transport properties of poly(benzophenone isophthalamide), DBF/ISO, poly(benzophenone‐5‐tert‐butylisophthalamide), DBF/TERT, homopolymers, and their copolyamides with different DBF/TERT ratios are reported. The results indicate that the glass transition temperatures of the copolyamides increase as the concentration of DBF/TERT in the polyamide increases. The gas permeability coefficients for DBF/ISO are around 10^?2 Barrers for O₂ which situates this polymer as a barrier polymer. It was also found that permeability coefficients in all polyamides and copolyamides are independent of pressure for He or decrease slightly particularly with O₂, CO₂, and N₂. It was seen that DBF/TERT is up to 15 times more permeable than DBF/ISO, depending on the gas being considered. This behavior was assigned to the presence of the bulky lateral substituent, the tert‐butyl group, in DBF/TERT and DBF/TERT‐co‐DBF/ISO copolyamides. This bulky substituent increases fractional free volume and interchain spacing; as a consequence, the gas permeability and diffusion coefficients generally increase. The experimental results for the gas permeability coefficients and permselectivity for the copolyamides was well represented by a semilogarithmic mixing rule of the homopolyamides permeability coefficients as a function of their volume fraction. The selectivity of gas pairs, such as He/O₂ and He/CO₂, decreased slightly with the addition of DBF/TERT. The temperature dependence of permeability for homopolyamides and copolyamides can be described by an Arrhenius type equation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2083–2096, 2007     

Optical filters with panchromatic emulsion layers for image processing

Amplitude filters with non-linear adaptive performance in the Fourier plane of a mirror optical system are considered. Panchromatic silver bromide layers with a printout effect are employed. The processing of binary and grey-scale images with the aid of a passively adaptive mirror filtering block is investigated.     

Characterization of polyplexes involving small RNA

The purpose of the present study is to provide a tool for an efficient design and synthesis of non-viral vectors for small RNA delivery. The effects of properties of the polycation, such as molecular weight, charge density and backbone structure, to polyplex structure and physicochemical behavior were systematically evaluated. The condensing agents, polyethylenimine (PEI), chitosan (CS) and poly(allylamine) (PAA) were added to sRNA molecules at different N/P ratio. The efficiency of encapsulation and protection of sRNA, as well as polyplex size, zeta potential and morphology were followed and compared. The results show that PEI/sRNA polyplexes display a small size and positive zeta potential. However, for low molecular weights, this polycation is unable to protect sRNA in the presence of a decompacting agent. With chitosan, sRNA is efficiently compacted at high N/P ratios. The CS/sRNA complexes display small sizes, ca. 200 nm, positive surface charge and also good stability. Finally, the PAA/sRNA polyplexes were found to be the smallest at low N/P ratios, displaying a good encapsulation efficiency and high stability. A rationale for the experimental observations is provided using Monte Carlo simulation for systems with polycations of different length and charge density. The simulations showed that there is an interplay between the size of polycation chains and its charge density that define the degree of condensation for sRNA.     

SQUID-based measuring systems

A program has been developed and initiated at the Indira Gandhi Centre for Atomic Research (IGCAR) for the utilization of SQUID sensors in various application areas. DC SQUID sensors based on Nb-AlO _x -Nb Josephson junctions have been designed and developed inhouse along with associated flux-locked loop (FLL) electronics. A compact low field SQUID magnetometer insertible in a liquid helium storage dewar has also been developed inhouse and is in use. Efforts to build a high field SQUID magnetometer, SQUID-DAC system, are in progress. A planar gradiometric DC SQUID sensor for non-destructive evaluation (NDE) application to be used in relatively unshielded environment has been designed and developed. An easily portable NDE cryostat with a small lift-off distance, to be used in external locations has been designed and tested. The magnetic field produced by a given two-dimensional current density distribution is inverted using the Fourier transform technique.     

Activation Energy of Light Induced Isomerization of Resveratrol

Isomerization of trans-stilbenes is known to be induced by light. The two isomers have distinct absorption, fluorescence excitation and emission spectra. Resveratrol, 3,4',5-trihydroxystilbene, is a member of the stilbene family. The interest of the scientific community in resveratrol has increased over the last years due to its biomedical properties. Whereas there is a growing confidence that trans-resveratrol is non-toxic, very little is known about the pharmacology of cis-resveratrol. Of this very reason there is considerable interest in knowing the energetics of the trans-cis conversion. Cis-resveratrol is characterized by a large fluorescence quantum yield when compared to trans-resveratrol. In the present paper we report a detailed analysis of the spectral changes induced in trans-resveratrol upon 260?nm excitation for different time periods. Spectral changes have been monitored with UV-visible absorption and steady-state fluorescence spectroscopy at pH?4 at 20, 25, 30, 35, 40, 45 and 50?°C. Continuous 260?nm excitation induces a blue shift in the absorption and fluorescence excitation spectra of resveratrol and a 14?nm blue shift in its fluorescence emission. The photoisomerization yield is reported as a function of 260?nm excitation time. 330?min continuous excitation led to ~60% isomerization yield. The kinetics of trans-cis isomerization has been monitored following the increase in fluorescence quantum yield upon continuous 260?nm excitation of trans-resveratrol. The study was carried out at the above mentioned temperatures in order to obtain the Arrhenius activation energy of photoisomerization. Activation energy and pre-exponential factor were 3.7?±?0.3?kcal.mol(-1) and 10.6?±?1.6 s(-1), respectively. The activation energy is comparable with previously reported values for the photoisomerization of other stilbenes.