Continuity of The Drazin inverse

Let A be an n×n matrix. It is shown that if a matrix  comes close to satisfying the definition of the Drazin inverse of A,A^D , then  is close to A^D .     

Band structure of superdeformed bands in odd-A Hg nuclei

Through particle-rotor model, band structure of superdeformed bands in odd-A Hg nuclei is analysed. An overall and excellent agreement between the calculated and observed kinematic and dynamic moments of inertia is obtained. The electromagnetic transition properties of SD bands can be used to identify the configuration with certainty     

Baum-Connes conjecture and coarse geometry

In this paper, we show that the Baum-Connes conjecture for a discrete group with coefficients inl (,K) is equivalent to the coarse Baum-Connes conjecture for as a metric space with a length metric. We apply this result to prove special cases of the Baum-Connes conjecture.Supported by DMS8505550 through a MSRI Postdoctoral Fellowship.     

Lower semicontinuity of some functionals under PDE constraints: An \mathcal{A}-quasiconvex pair

The problem of establishing necessary and sufficient conditions for l.s.c. under PDE constraints is studied for a special class of functionals:

Coherent production of pions in high energy π−-interactions

From an analysis of 12 ‘clean’ pion tridents produced in 17.2 GeV/c π^?-interactions in emulsion nuclei, the distributions of the longitudinal and transverse momentum of recoil nuclei are obtained. The distribution of transverse momentum of recoil nuclei for the combined data of Caforioet al., Azimovet al., and the present experiment is compared with the expected curves for various assumptions. It is demonstrated that the best fit is for the assumptions (a) only light nuclei contribute to the coherent process and (b) all nuclei contribute equally. It is stressed that the conclusion of Caforioet al., that the light nuclei do not play an important role is based on the discrepancy between the observed and expected mean free path which is critically hinged on the cross-section obtained in the heavy liquid bubble chamber—a cross-section whose value is uncertain.     

He3 nuclei in the low energy primary cosmic radiation

The flux of He³ nuclei and the ratio He³/(He³+He⁴) in the low energy primary cosmic radiation have been determined using a stack of nuclear emulsions exposed at 3·1 g. cm.^?2 of atmospheric depth from Fort Churchill, Canada, in June 1963. The grain-densityversus residual range method was used to determine the masses of the helium nuclei. Using a sample of 146 helium nuclei whose masses could be identified, the ratio He³/(He³+He⁴) is obtained as 0·14±0·04 for the kinetic energy interval 115–210 MeV per nucleon and 0·43±0·11 for the rigidity interval 0·85–1·05 BV. The differential fluxes of He³ nuclei are determined as 0·017±0·006, 0·045±0·015, and 0·054±0·017 particles/M². Sr. Sec. MeV/nucleon, in the kinetic energy intervals of 117–183, 183–217, and 217–250 MeV/nucleon respectively. These results are compared with those of other investigators. From the results of the present work the amount of matter traversed in space by the primary cosmic ray helium nuclei of energy 115–210 MeV/nucleon is obtained as 4·7±1·8 gm. cm.^?2 of hydrogen.     

Special point sets inPG(n,q) and the structure of sets with the maximal number of nuclei

The structure of _{n– 1}-sets inPG(n, q) with more thanq – 1 nuclei is investigated. It is shown that classification of these sets with the maximal numberq ^{n– 1}-q ^{n– 2} of nuclei is equivalent to the classification of (q + l)-sets inPG(2,q) havingq –1 nuclei.Dedicated to Professer Walter Benz for his 60^th birthday     

Rigidity spectrum of cosmic ray helium nuclei

An experiment has been carried out using an oriented stack of nuclear emulsions to determine the rigidity spectrum of cosmic ray helium nuclei between 12 and 40 GV, by taking advantage of the variation of the geomagnetic cut-off rigidity in the east-west plane over Hyderabad, India. Altotal of 2433 identified helium nuclei recorded in the stack, has been divided into 8 angular intervals in the east-west plane corresponding to 8 different cut-off rigidities. From this the integral fluxes of helium nuclei at the top of the atmosphere have been obtained for all the 8 rigidity intervals. The vertical flux above an effective threshold rigidity of 16·73 GV has been determined with high statistical accuracy and has a value of 15·0±0·5 helium nuclei (m².sr.sec.)^?1. The rigidity spectrum of these nuclei between 12 and 40 GV can be well represented by a power law of the type N (>R) =1990 R^?1.74±0.11 (m².sr.sec.)^?1 and is the first direct determination so far made in this rigidity region. The differential rigidity spectra of protons, helium nuclei and S-nuclei of the cosmic radiation in the vicinity of the earth at solar minimum (1965) have been constructed with the existing world data and it is found that for rigidities ? 10 GV, the three spectra have, within experimental errors, the same slope of 2·6. The ratio P/He and He/S of the differential fluxes have been studied as a function of rigidity. It is found that for R>2 GV, the ratio P/He has, within experimental errors, a constant value of 6·3; as for the ratio He/S, it seems that the experimental data above a GV is not inconsistent with a constant value of 14 over the entire rigidity interval considered here.     

Approximation of the bifurcation function for elliptic boundary value problems

The bifurcation function for an elliptic boundary value problem is a vector field B(ω) on R ^d whose zeros are in a one‐to‐one correspondence with the solutions of the boundary value problem. Finite element approximations of the boundary value problem are shown to give rise to an approximate bifurcation function B^h(ω), which is also a vector field on R ^d. Estimates of the difference B(ω) − B^h(ω) are derived, and methods for computing B^h(ω) are discussed. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 194–213, 2000     

Systematics of some beta-transitions

0⁺ excited states of even-even nuclei can arise in several ways. In order to throw some light on the mechanism of excitation of these states, the log (ft) values for beta-transitions to the 0⁺ excited state and the 0⁺ ground state of even-even nuclei have been compared. In this analysis both allowed and forbidden beta-transitions have been considered. This survey is similar to that of beta-transitions by M. Sakai. Results of the present analysis are presented and compared to that of Sakai.     

Investigations on the multiply charged nuclei of the primary cosmic radiation near the geomagnetic equator using nuclear emulsion

A nuclear emulsion stack was exposed over Hyderabad, India (geomagnetic latitudeλ=7·6° N) under a mean atmospheric depth of 6·8 g./cm.², on 24 March 1960. The relative and absolute intensities of Be and B nuclei and nuclei of charge Z?6 (the S-nuclei) have been determined in this stack. The intensities were extrapolated to the top of the atmosphere using measured fragmentation parameters involved in collisions of cosmic ray nuclei in graphite. The flux values of Be, B and S nuclei at the top of the atmosphere have been determined to be 0·025±0·011, 0·101±0·023 and 1·12±0·10 particles/m.² sec. sr. respectively. The ratios of intensities B/S, Be/S and Be/B have been found to be 0·09±0·02, 0·022±0·008 and 0·25±0·11 respectively. These ratios of intensities have been used (a) to compute the amount of matter traversed by the radiation before reaching the vicinity of the earth as 2·6±0·6 g./cm.², (b) to show that the Fermi mechanism of acceleration of particles is not efficient at these energies (1–10 GeV/n.) in interstellar space and (c) to show that preferential acceleration of H₁-nuclei (Z?20) is not of overwhelming importance. The derived source composition of nuclei of energy ?7·5 GeV/n suggests that N, O, F and H₃-nuclei (Z=10–15) have similar abundances in the universe and in cosmic rays, and that C and H₁-nuclei are overabundant in cosmic rays.     

Some remarks on the E2-M1 mixing ratios of 2′→2 transitions in even-even nuclei

Experimental values of E₂-M₁ mixing ratios of 2′⁺→2⁺ transitions in even-even nuclei are found to decrease with increasing splitting of 2′⁺ and 4⁺ levels.     

Sur le theoreme de Stone-Weierstrass en Algebre commutative

We show that the sufficient conditions given by Cahen, Grazzini and Haouat for a version of the Stone-Weierstrass theorem in commutative algebra are the widest. More precisely, letA be a Noetherian ring andI a proper ideal ofA such thatA is Hausdorff with respect to theI-adic topology. Note the completion ofA andC(Â,Â) the ring of continuous functions from to with uniform convergence topology. The subset of polynomial functions is dense inC(Â,Â) if and only if the radical ofI is a maximal idealm ofA and the local ringA _m is a one-dimensional analytically irreducible domain with finite residue field.     

Nuclear disintegrations produced in nuclear emulsions by α-particles of great energy

A study of nuclear disintegrations caused by α-particles of primary cosmic radiation with energies > 5 BeV per nucleon, has been carried out. In a systematic survey in nuclear emulsions using ‘along the track’ scanning method, 479 α-particles with a total track length of 40·84 metres and 242 interactions were obtained. From the angular distribution of shower particles associated with these interactions, a procedure has been found for distinguishing protons, which originally formed part of the incident α-particle and which have not taken part in the interaction, from other charged particles. The mean free path for nuclear interaction in G-5 emulsion is found to be 17·5±1·1 cm. (68·9±4·3 gm./cm.²). Assigning both to the incident α-particle and to the target nuclei a radius R=r _oA^1/2, one obtains an effective nuclear radiusr _o=1·13±0·04 ×10^?13 cm. Using the number of protons emerging from disintegrations of heavy nuclei (Silver and Bromine) without having participated in the interaction (as can be deduced from the angular distribution) and assuming spherical nuclei of uniform density, the mean free path of nucleons in nuclear matter is calculated to be less than 3·2×10^?13 cm.     

Embedding relations connected with strong approximation of Fourier series

We consider the embedding relation between the class W ^q H _β ^ω , including only odd functions and a set of functions defined via the strong means of Fourier series of odd continuous functions. We establish an improvement of a recent theorem of Le and Zhou [Math. Inequal. Appl. 11(4) (2008) 749–756] which is a generalization of Tikhonov’s results [Anal. Math. 31 (2005) 183–194]. We also extend the Leindler theorem [Anal. Math. 31 (2005) 175–182] concerning sequences of Fourier coefficients.     

Modulation of galactic cosmic radiation in interplanetary space by the solar wind

The effect of solar wind on the relative abundances of galactic cosmic rays is assessed using the theories proposed by Parker¹ and Dorman.² The modulation factors for the ratios of electrons, deuterons, tritons and helium nuclei to protons, helium-3 to helium-4 and light (Z=3–5) to medium nuclei (Z=6–9) are presented. The effect of the modulation on the differential energy spectra is studied. The form of the spectra, the position of the maximum in the spectra and the relative reduction over a solar cycle place a restriction on the parameters in the solar wind theory. Starting with plausible galactic spectra and by varying the parameters it is possible to fit the form of the solar minimum spectrum but it does not seem possible to produce the relative reduction between minimum and maximum throughout the energy range, with in the framework of the present solar wind theory.     

Rings over which all modules are semiregular

For a ring A, it is proved that all A-modules are semiregular if and only if A is an Artinian serial ring and J ²(A) = 0. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 2, pp. 185–194, 2007.     

The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree

It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We study the planar slope number, i.e., the minimum number of distinct edge-slopes in such a drawing of a planar graph with maximum degree Δ. We show that the planar slope number of every planar partial 3-tree and also every plane partial 3-tree is at most O(Δ ⁵). In particular, we answer the question of Dujmovi? et al. (Comput Geom 38(3):194–212, 2007) whether there is a function f such that plane maximal outerplanar graphs can be drawn using at most f(Δ) slopes.     

Pulsanregung von Hg. Ionenlaserlinien

In gepulsten Hg Niederdruckentladungen ohne Fremdgaszusatz konnten vier sichtbare und erstmals auch 14 ultraviolette Ionenübergänge zur Lasertätigkeit angeregt werden. Zur Untersuchung des Lasermechanismus wurden bei Entladungsdurchmessern von 7 mm, 10 mm und 30 mm die Pulsdauern im Bereich 10 sec<<5 msec und der Hg Fülldruckp im Bereich 10^–3 torr<p<10^–2 torr variiert. Die gemessenen Strahlungsleistungen der ultravioletten Hg II Linien lagen im mW-Bereich, während jeder der drei sichtbaren Hg III Uebergänge Leistungen im Bereich 10–100 Watt lieferte.     

Analysis of some allowed beta-transitions

Sakai’s method of analysing logft values has been extended to higher excited states in even-even nuclei. Within the context of the rather limited data an enhancement in the matrix element is observed for transitions to 2″⁺, 2?⁺ and 4′⁺ and 4″⁺ levels.