Ratio of pions to protons and ratio of neutral to charged interacting particles at mountain altitude of 800 gm/cm2

Using a combined set-up of a multiplate cloud chamber, an air Cerenkov counter and a total absorption spectrometer, the ratio of pions to protons not associated with large air showers has been determined to be 0·50 ± ·07 in the energy region 20–40 GeV at an altitude of 800 gm/cm². In the same energy region the ratio of neutral to charged particles is found to be 0·66 ± ·07. From the ratio of neutrons to protons deduced from these measurements (i.e., 0·99 ± ·11), it is concluded that most of the charge excess of nuclear active particles of energies > 20 GeV at mountain altitudes and sea-level is due to pions.     

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.     

Time structure of the hadronic component of extensive air showers

Proceedings - Mathematical Sciences - A detailed study of the time structure of hadrons of energy > 5 GeV in extensive air showers has been carried out at Ootacamund (8·00 gm/cm2) using...     

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.     

Fourier-Stieltjes transforms of measures with a certain continuity property

Let G be a compact abelian group whose dual group Γ has a finite torsion subgroup. Let μ?M(G) such that ¦μ ¦assigns no mass to any coset of any closed subgroup of G whose index is infinite. Then there is d > 0, dependent only on ∥ μ ∥, such that if for each $\text{γ ? Γ, ¦}\text{}\text{?}\text{gm(γ)¦ ? 1}\text{or}\text{¦}\text{}\text{?}\text{gm(γ)¦ ? d}$, then the set $\text{{γ: ¦}\text{}\text{?}\text{gm(γ)¦ ? 1}}$ is finite. An upper bound on the cardinality of this set is obtained in terms of ∥ μ ∥and the cardinality of the torsion subgroup of Γ.     

Heats of combustion of some symmetrical dialkyl ureas and their corresponding alkyl carbamates

The standard heats of combustion of the disubstituted ureas, N, N′-diheptyl urea, N, N′-dioctyl urea and N, N′-didecyl urea and the carbamates,n-heptyl ammoniumn-heptyl carbamate,n-octylammoniumn-octyl carbamate andn-decyl ammoniumn-decyl carbamate have been determined. The values found are 2353±1·3, 2658·4±1·1, 3268·5±1·7, 2349·8±1·6, 2654·4±1·2, 3264·6±1·8, K.cals. mole^?1 respectively. The heats of formation of these compounds have been calculated.     

Periodicities in the series of cyclonic disturbances over India

The time series of yearly occurrence frequency of cyclonic disturbances over the Indian region for 1891–1970 is subjected to power spectrum analysis by the maximum entropy method (MEM) of Burg. Earlier analyses by the conventional Blackman-Tukey method had indicated periodicities atT= 2·3-2·5, 5 and 30–45 years at about 90–95% significance level. The present analysis shows peaks atT = 1·2, 2·4, 2·9, 3·7, 4·7, 6·4, 7·4, 9·2, 10·5, 20 and 40–60 years but the significance level may not be better than the earlier method. When data are analysed separately for first half and latter half, periodicities observed are quite different, the earlier half revealingT= 1· 2, 2·3, 2·9, 4·7, 9·0 and 23 years and the latter half revealingT= 1·2, 2·1, 2·4, 3·8, 6·7 and 21 years. Thus, a change of pattern before and after about 1920 is indicated. However, the power in the various peaks is small and a random origin cannot be ruled out. An analysis of several artificially produced samples of pseudo-Gaussian random white noise of the same mean, standard deviation and length (80 values) as the above physical samples indicated that similar peaks could occur by pure chance also. Physically, T=l·2 years corresponds to the Chandler’s wobble and other peaks could be harmonics of the sunspot cycleT= 11 years or double sunspot cycleT = 22 years. However, no peak is noticed at or nearT= 11 years whereasT near 22 years is noticed.     

Distribution of Arithmetic Functions on Particular Subsets of Integers

Lithuanian Mathematical Journal - Let Q1, . . . , Qt ∈?[x] be polynomials with no constant term for which each linear combination m1Q1(x) + · · ·+mtQt (x) with m1, . . ....     

Microwave spectrum of pentafluorobenzonitrile

The absorption spectrum of pentafluorobenzonitrile has been investigated in the frequency range of 18–26·5 GHz using a 100 KHz stark modulated microwave spectrometer. The analysis of the spectrum is based on the rigid asymmetric rotor theory. The rotational constants obtained are A=1026·82±0·3 MHz, B=776·34±0·1 MHz, C=442·06±0·1 MHz and the asymmetry parameterχ=+0·1433. The inertial defect is I _o ?I _a ?I _b =0·081 amu Ų. The bond distances ared _CF=1·328 Å andd _CN=1·157 Å. The results are in good agreement with the assumed planarity of the molecule and the normal values of bond distances.     

两个Smarandache复合函数的混合均值公式

对任意正整数n,Smarandache函数U(n)、V(n)定义为:U(1)=V(1)=1,n>1时,若它的标准分解式是n=p_1~(α_1)p_2~(α_2)…p_r~(α_r),U(n)=1{α_1·p_1α_2·p_2,…,α_r·p_r};V(n)={α_1·p_1,α_2·p_2,…,α_r·p_r}.研究了这两Smarandache函数U(n)与V~m(n)的值分布,并用初等方法及素数分布定理得到了几个较强的渐近公式.     

Energy transfer to neutral pions in high energy nuclear interactions

The fraction of energy transferred to the neutral pions ( \( K_{\pi ^ \circ } \) ), in an interaction of high energy (> 20 GeV) N-particles (nucleons and pions) with atomic nuclei, is estimated from the data collected, using a total absorption spectrometer (TAS) and a multiplate cloud chamber. The average value of \( K_{\pi ^ \circ } \) ( \( \bar K_{\pi ^ \circ } \) ) is found to be 0·12 ± 0·01 in the energy range 20–100 GeV (ē₀ = 35 GeV) and 0·19 ± 0·02 in the region of > 100 GeV (ē₀ = 206 GeV). The value of \( \bar K_{\pi ^ \circ } \) obtained in different experiments and its dependence on the primary energy are discussed. An increase in \( \bar K_{\pi ^ \circ } \) in pion-nucleus collisions with the energy of the pion or an increase in the ratio of pions to protons, at 800 gm./cm.², in the energy range of a few tens of GeV to a few hundred GeV or both is to be invoked to explain the energy dependence of \( \bar K_{\pi ^ \circ } \) observed in this investigation.     

A polarographic study of methionine complexes of cadmium in mixed solvents

Methionine complexes of cadmium in 25 and 50 per cent aqueous mixtures of ethyl and methyl alcohol and dioxan have been studied. The half-wave potentials measured in both the alcohols were the same and the reduction was reversible. Three complex species withβ ₁=1·0×10⁴,β ₂=1·1×10⁷ andβ ₃=1·2×10⁹ were found in 25 per cent alcohol while four complexes withβ ₁=3·0×10⁴,β ₂=4·3×10⁷,β ₃=4·0×10⁹ andβ ₄=1·6×10¹¹ were observed in 50 per cent solutions. In the case of dioxan, the reduction was quasi-reversible (k _s=1·0×10^?3 cm sec^?1) in 25 per cent and irreversible (k _s=2·0×10^?4 cm sec^?1) in 50 per cent solutions. The stability constants, evaluated using the formal potentials, wereβ ₁=7·0×10³,β ₂-3·9×10⁵;β ₂=3·9×10⁸ andβ ₄=3·4×10¹⁰ in 25 per cent dioxan andβ ₁=1·5×10⁴,β ₂=3·4×10⁷.β ₃=7·5×10⁹ andβ ₄=9·0×10¹¹ in 50 per cent solutions.     

Degree sequences of graphs and dominance order

Suppose that the graphical partition H(A) = (a₂¹ ≥ ··· ≥ a_n¹) arises from A = (a₁ ≥ ··· ≥ a_n) by deleting the largest summand a₁ from A and reducing the a₁ largest of the remaining summands by one. Let (a_i+1′ ≥ ··· ≥ a_n′) = H′(A) denote the partition obtained by applying the operator H i times. We prove that the dominance order of partitions is preserved when we switch from A to (a₁ ≥ a₂¹ ≥ ··· ≥ a_i+1′ ≥ ···) =: E(A). This generalizes a recent result by Favaron, Mahéo, and Saclé on the residue of a graph. © 1996 John Wiley & Sons, Inc.     

Microwave spectrum of pentafluorobenzene

The microwave spectrum of pentafluorobenzene has been measured in the frequency region 12·5 to 18·00 KMHz. The spectrum is analysed on the basis of rigid asymmetric rotor theory. The rotational constants obtained are A=1471·963 MHz, B=1026·278 MHz, C=604·693 MHz and the asymmetry parameterκ=?0·0278. The inertial defect is Δ=I _c -I _a -I _b =?0·014 amu Ų. The bond distances ared _CF=1·328 Å andd _CH=1·089 Å, assumingd _CC=1·395 Å.     

A polarographic study of methionine complexes of cadmium and indium

The stability constants of methionine complexes of cadmium were determined polarographically by ths method of DeFord and Hume as β₁ =6·5 × 10³, β₂ = 1·7 × 10⁶ and β₃ = 2·1 · 10⁸. The indium complexes were studied by the modified method of Momoki and Ogawa and two complexes, with β₁ = 1·7 × 10⁸ and β₂ = 8·4 × 10¹³, were identified in the concentration range studied. The haf-wave potential of uncomplexed indium ion which cannot be measured directly owing to the irreversible nature of the reduction was calculated as — 0·503 Vvs. SCE.     

Semisummands and semiideals in banach spaces

Let |·| be a fixed absolute norm onR ². We introduce semi-|·|-summands (resp. |·|-summands) as a natural extension of semi-L-summands (resp.L-summands). We prove that the following statements are equivalent. (i) Every semi-|·|-summand is a |·|-summand, (ii) (1, 0) is not a vertex of the closed unit ball ofR ² with the norm |·|. In particular semi-L ^p-summands areL ^p-summands whenever 1<p≦∞. The concept of semi-|·|-ideal (resp. |·|-ideal) is introduced in order to extend the one of semi-M-ideal (resp.M-ideal). The following statements are shown to be equivalent. (i) Every semi-|·|-ideal is a |·|-ideal, (ii) every |·|-ideal is a |·|-summand, (iii) (0, 1) is an extreme point of the closed unit ball ofR ² with the norm |·|. From semi-|·|-ideals we define semi-|·|-idealoids in the same way as semi-|·|-ideals arise from semi-|·|-summands. Proper semi-|·|-idealoids are those which are neither semi-|·|-summands nor semi-|·|-ideals. We prove that there is a proper semi-|·|-idealoid if and only if (1, 0) is a vertex and (0, 1) is not an extreme point of the closed unit ball ofR ² with the norm |·|. So there are no proper semi-L ^p-idealoids. The paper concludes by showing thatw*-closed semi-|·|-idealoids in a dual Banach space are semi-|·|-summands, so no new concept appears by predualization of semi-|·|-idealoids.     

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.     

Low energy gamma-ray measurements over Hyderabad,India

The results of the first low energy gamma-ray (0.2 to 1 MeV) measurements at equatorial latitudes conducted by two-balloon flights over Hyderabad, India (7.6° N GM), are presented. The energy resolution of the detectors was sufficient to detect the γ-ray peak at 0.5 MeV due to the electron-positron annihilation. The flux of the 0.5 MeV photons was found to be 0.090 ± 0.012 photons/cm² sec at an atmospheric depth of 10 gm cm² and 0.048 ± 0.011 photons/cm² sec at the top of the atmosphere. Comparison of our results with those obtained at higher latitudes, show the existence of a considerable latitude variation of the 0.5 MeV flux, about a factor of 4 between 55° and 7° latitudes at an altitude of 10 gm/cm².     

Spectrophotometric studies of copper (II)—bis-2-pyridyl glycol complex

An aqueous solution ofbis-2-pyridyl glycol forms a deep blue water-soluble complex with an aqueous solution of copper (II) salts. The complex has an absorption maximum at 600–650 mµ between pH range 3·0–8·7. The complex is stable for four days and obeys Lambert-Beer’s law in the concentration range of 5·08–50·80 ppm. of copper (II) in solution. The optical density of the complex remains constant between pH 3·8–5·9. The molar composition as determined by the method of continuous variation and by the slope ratio method has been found to be 1:1. The limits of interference due to some foreign ions during the estimation of copper (II) have been determined.     

Some Results on p-Nilpotence and Supersolvability of Finite Groups

Let G be a finite group. A subgroup K of a group G is called an ?-subgroup of G if N _G (K) ∩ K ^x  ≦ K for all x ? G. The set of all ?-subgroups of G will be denoted by ?(G). Let P be a nontrivial p-group. A chain of subgroups 1 = P ₀ ? P ₁ ? ··· ? P _n  = P is called a maximal chain of P provided that |P _i : P _i?1| = p, i = 1, 2, ···, n. A nontrivial p-subgroup P of G is called weakly supersolvably embedded in G if P has a maximal chain 1 = P ₀ ? P ₁ ? ··· ? P _i  ? ··· ? P _n  = P such that P _i  ? ?(G) for i = 1, 2, ···, n. Using the concept of weakly supersolvably embedded, we obtain new characterizations of p-nilpotent and supersolvable finite groups.