Characteristics of high energy interactions I. High energy gamma-ray spectra near the top of the atmosphere

An emulsion chamber was used to study the characteristics of high energy nuclear interactions from the production spectra ofγ-rays. The emulsion chamber, which comprised of two parts, namely the detector and the graphite producer unit, was exposed to cosmic rays for about 7 hr at an atmospheric depth of 10 g cm⁻² at Hyderabad (geomagnetic latitude 7·6°N). 720 electromagnetic cascades due toγ-rays were recorded in the detector. These cascades were classified into three groups; (a)γ-rays from nuclear interactions in the detector (b)γ-rays from nuclear interactions in the producer unit and (c)γ-rays of atmospheric origin. The energies of the cascades were determined using photometric method. The spectra ofγ-rays from groups (a) and (c) were determined and compared with similar spectra obtained at greater atmospheric depths. The spectra were found to obey a power law. The spectrum ofγ-rays of atmospheric origin was found to steepen at high energies,E _r>2200 GeV.     

Optical characterization of the silicon photodiodes for the establishment of national radiometric standards

Optical properties of the silicon photodiodes are investigated in the visible spectral regime. Non-linearity measurement standard was established by using Hamamatsu S1337-11 type windowless silicon photodiode whose non-linearity value was found to be better than 6×10⁻⁵ at photocurrent level of 10⁻⁹ to 10⁻⁴ A. Temperature effects on the spectral responsivity for S1337-11, S1337-1010BQ and S1227-1010BQ type photodiodes were analyzed between 20°C and 40°C at 488.1, 514.7 and 632.8 nm vacuum wavelengths. The spatial uniformities of the responsivity for three type photodiodes are performed with a laser beam having 1 mm diameter by using home made two-axis micro translation system. Results of the reflectance measurements for three elements of reflection-based trap detectors were compared with the predicted values obtained from Fresnel equations.     

Lower bounds for boundary roughness for droplets in Bernoulli percolation

We consider boundary roughness for the ``droplet' created when supercritical two-dimensional Bernoulli percolation is conditioned to have an open dual circuit surrounding the origin and enclosing an area at least l², for large l. The maximum local roughness is the maximum inward deviation of the droplet boundary from the boundary of its own convex hull; we show that for large l this maximum is at least of order l^1/3(logl)^–2/3. This complements the upper bound of order l^1/3(logl)^–2/3 proved in [Al3] for the average local roughness. The exponent 1/3 on l here is in keeping with predictions from the physics literature for interfaces in two dimensions. The research of the first author was supported by NSF grant DMS-9802368. The research of the second author was supported by NSF grants DMS-9802368 and DMS-0103790.Mathematics Subject Classification (2000): Primary 60K35; Secondary 82B20, 82B43     

Analytical computation of the eigenvalues and eigenvectors in DT-MRI

In this paper a noniterative algorithm to be used for the analytical determination of the sorted eigenvalues and corresponding orthonormalized eigenvectors obtained by diffusion tensor magnetic resonance imaging (DT-MRI) is described. The algorithm uses the three invariants of the raw water spin self-diffusion tensor represented by a 3 x 3 positive definite matrix and certain math functions that do not require iteration. The implementation requires a positive definite mask to preserve the physical meaning of the eigenvalues. This algorithm can increase the speed of eigenvalue/eigenvector calculations by a factor of 5-40 over standard iterative Jacobi or singular-value decomposition techniques. This approach may accelerate the computation of eigenvalues, eigenvalue-dependent metrics, and eigenvectors especially when having high-resolution measurements with large numbers of slices and large fields of view.     

Vibrational dynamics of the organometallic compound triarylorganoantimony (V) SbPh<Subscript>3</Subscript>[O<Subscript>2</Subscript>CC(OH)Ph<Subscript>2</Subscript>]<Subscript>2</Subscript>

A complete normal coordinate analysis was performed for five-coordinate non-rigid triarylantimony diester SbPh₃(O₂CR)₂, known to be a bioactive molecule, using Wilson G-F matrix method and Urey Bradley force field. The study of vibrational dynamics was performed using the concept of group frequencies and band intensities.      

Thermoelectric effects in organic conductors in a strong magnetic field

The linear response of the electron system of a layered conductor to the temperature gradient in this system in a strong magnetic field is investigated theoretically. Thermoelectric emf is studied as a function of the magnitude and orientation of a strong external magnetic field; the experimental investigation of this function, combined with the study of the electric and thermal resistance, allows one to completely determine the structure of the energy spectrum of charge carriers.     

Phosphonobetaine/sulfur dioxide copolymer by Butler’s cyclopolymerization process

The zwitterionic monomer, ethyl 3-(N,N-diallylammonio)propanephosphonate and sulfur dioxide were cyclocopolymerized in DMSO using azobisisobutyronitrile or ammonium persulfate as initiators to afford a pH-responsive polyphosphonobetaine/SO₂ (PPB/SO₂) copolymer. The polymers, on treatment with HCl and NaOH, gave the aqueous solutions of the corresponding cationic polyphosphononic acid (CPP) and anionic polyphosphonate (APP). The solution properties of the PPB having two pH-responsive functionalities were investigated in detail by potentiometric and viscometric techniques. Basicity constants of the amine and phosphonate groups in APP were found to be “apparent” and as such follow the modified Henderson–Hasselbalch equation. The incorporation of SO₂ moiety has resulted in the decrease of basicity constant of the nitrogens in the copolymer by staggering ?2 units of log K in compare to that of the corresponding homopolymer. The basicity difference is expected to have an effect on the chelating properties of the polymers. In contrast to many polycarbo- and -sulfobetaines, the PPB was all found to be soluble in salt-free water as well as in salt (including Ca²⁺ and Li⁺)-added solutions. The PPB demonstrated ‘antipolyelectrolyte’ viscosity behavior and found to have higher viscosity values in LiCl than in NaCl or NaI.     

Spectrophotometric and spectrofluorimetric investigation of different equilibria of a recently synthesized Schiff base with the aid of chemometric methods

In this study ground and excited states acidic dissociation constants of a recently synthesized Schiff base was obtained in a DMF:water mixture of 30:70 (v/v) using absorption and fluorescent spectra of the Schiff base in different pH values with the aid of chemometric methods. In addition, the fluorescent of the two kinds of tautomers of this Schiff base was investigated and the rate of tautomerization was obtained using rank annihilation factor analysis (RAFA). The effect of different kinds of surfactants such as sodium dodecyl sulfate (SDS), cetyltrimethylammonium bromide (CTAB) and Triton X-100 on fluorescence spectrum of the Schiff base in a DMF:water mixture of 2:98 (v/v) was investigated. CTAB increased the fluorescence intensity of the Schiff base while SDS and Triton X-100 had no significant effect on it. β-Cyclodextrin increased the fluorescence intensity of the Schiff base. Also the sensing behavior of this Schiff base toward metal ions was studied in DMF and ethanol by fluorescence spectroscopy. The Schiff base showed prominent fluorescent signal in the presence of Zn²⁺, whereas other metal ions failed to induce response and ground-state dissociation constant of the complex was determined by direct fluorimetric titration as a function of Zn²⁺ concentration.     

Bis­(acesulfamato)­tetra­aqua­cobalt(II)

The crystal structure of the first acesulfame–metal complex, namely tetra­aqua­bis­[6‐methyl‐1,2,3‐oxa­thia­zin‐4(3H)‐onato 2,2‐dioxide‐κN]­cobalt(II), [Co(C₄H₄NO₄S)₂(H₂O)₄], is re­ported. The Co^II ion resides on a twofold axis and is coordinated by four aqua ligands defining the basal plane and by two monodentate acesulfamate ligands, via their ring N atoms, in the axial positions. Two intra‐ and three intermolecular hydrogen‐bonding interactions stabilize the crystal structure and form an infinite three‐dimensional lattice.