A lower bound on the error in dimensionality reduction resulting from projection onto a restricted subspace

We obtain the lower bound on a variant of the common problem of dimensionality reduction. In this version, the dataset is projected on to a k dimensional subspace with the property that the first k-1 basis vectors are fixed, leaving a single degree of freedom in terms of basis vectors.     

Simultaneous determination of bergenin and gallic acid in Bergenia ligulata wall by high-performance thin-layer chromatography

A simple and reproducible high-performance thin-layer chromatographic method was developed for the simultaneous determination of bergenin and gallic acid in Bergenia ligulata. Water and methanol were used as the extracting solvents. The concentrations of bergenin and gallic acid in both of these solvents were found to be almost the same. The method involves separation of the components by thin-layer chromatography on a precoated Silica Gel 60 F254 plate with a solvent system of ethyl acetate-formic acid-acetic acid-water (100 + 11 + 11 + 27). The sensitivity of the method for bergenin was 0.30 microg, whereas for gallic acid it was 0.25 microg. The proposed method is precise and sensitive and can be used for the detection, monitoring, and simultaneous quantification of bergenin and gallic acid in B. ligulata.     

Simultaneous determination of thermal conductivity and diffusivity of porous materials

The theory of temperature variation at any point in an infinitely extending medium containing an infinitely long thin conducting wire, heated periodically, is applied to a probe having finite dimensions and thermal properties. The conditions for a minimal effect due to finite dimension of the medium and contact resistance between the probe and medium are discussed. The results of thermal conductivity and diffusivity, thus obtained, are reported. The thermal probe method under periodic conditions gives satisfactory results.     

Titration curves of p-aminobenzoic acid–formaldehyde polymer in relation to its structure

p-Aminobenzoic acid and formaldehyde were condensed in the presence of acid catalyst. The linear condensation polymer thus obtained was then separated into four fractions by a fractional precipitation method. Conductometric titrations were carried out on these four polymer fractions and the conglomerate in nonaqueous solvents with acid as well as base. The titration curves indicated a large number of additional breaks before the complete neutralization of COOH or NH₂ groups. These observations have been interpreted in terms of degree of polymerization and the structure of the polymer.     

Characteristics of high energy interactions II. Production spectra of Gamma-rays in graphite

Twenty high energy nuclear interactions produced in the graphite units of an emulsion chamber were recorded. The emulsion chamber was exposed to cosmic rays at an atmospheric depth of 10 g cm⁻² for about 7 hr over Hyderabad, India. Fourteen interactions which radiated energyΣ E _r⩾1000 GeV in the form ofγ-rays were analysed in detail. The median energy 〈Σ E _r〉 of the interactions was 1600 GeV. Results concerning the multiplicity, the transverse and longitudinal momentum distributions, and the fractional energy distribution ofγ-rays in these interactions are presented. The average transverse momentum ofπ ⁰—mesons <pt _π ⁰> is found to increase very slowly with the primary energyE ₀ and it can be approximated by the function <pt _π ⁰>=0·238E ₀ ^0.06 .     

Analysis of polarizabilities of alkali halides using Narayan-Ramaseshan repulsive potential

The repulsive potential in ionic crystals recently proposed by Narayan and Ramaseshan (NR) can be expressed as the sum of the contributions from the individual ions. In the present paper we show that using this repulsive potential it is possible to divide the polarizability arising from the relative displacement of ions into its ionic constituents. NR have also derived the ionic radii in alkali halides which we have used to estimate the electronic polarizabilities of ions with the help of polarizability-radius cube relation. The electronic polarizabilities of alkali and halogen ions thus evaluated show a good agreement with those deduced from the experimental refraction data.     

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.     

Angular spectrum approach to electromagnetic wave propagation in inhomogeneous media

The angular spectrum representation of the electromagnetic wave field is employed to solve the wave propagation in a weakly inhomogeneous medium. Taking the two-dimensional spatial Fourier transform of the radiation field as well as of the dielectric constant, the angular amplitude is shown to satisfy an integro-differential equation. A similar equation is also applicable for the propagation of radiation in a non-linear medium. This integro-differential equation is solved for two specific cases of interest, namely that of a stratified medium and of a square-law medium.     

Theory of the sticking coefficient for atom-surface scattering

A calculation of the sticking coefficient is presented for a one-dimensional system with harmonic interactions. The physical basis for the results is discussed and it is shown how general conclusions may be drawn for three-dimensional systems.