Emission spectrum of chlorine excited in the presence of argon

The spectrum of chlorine excited in the presence of argon has been photographed with a 21-ft. grating spectrograph in the first order. Two band systems in the region 2600–2390 Å and 2365–2239 Å are observed which appear to be respectively analogous to the 2950–2670 Å and 2660–2590 Å systems of bromine reported earlier by Venkateswarlu and Verma. The wavelengths and the wavenumbers of all the bands in the system 2600–2390 Å are given. The vibrational scheme along with the corresponding Franck-Condon parabola is also given. The analysis suggests that the lower state of the system is the 3π(O _u ⁺_ state established by Elliott at 17658 cm.^?1 and that the upper state is at 67773 cm.^?1 The vibrational constants obtained arew ₀′ = 246·6 cm.^?1,w ₀′x ₀′ = 0·615 cm.^?1,w ₀″ = 255·2 cm.^?1,w ₀″x ₀″ = 5·5 cm.^?1,w ₀″y ₀″ = ?0·0155 cm.^?1 andw ₀″z ₀″ = 0·00115 cm.^?1     

The emission spectrum of iodine bromide excited in the presence of Argon

IBr vapour was excited in the presence of argon by an uncondensed transformer discharge. Four band systems were obtained in the regions 5425–5360 Å, 4520–4415 Å, 4120–4010 Å and 3915–3540 Å of which the first three are discussed in this paper. The wavelengths and wavenumbers of the band heads in three systems as measured from the plates obtained with a 3-prism Steinheil glass spectrograph are given along with their visually estimated relative intensities. The three band systems, which are new, are analysed and the following vibrational constants expressed in cm.^?1 are obtained:

Band system	v e	w e ″	w e ″x e ″	w e ″y e ″	w e ′	w e ′x e ′
5425-5360 Å	18613	65·5	0·24	?0·01	43·0	0·026
4520-4415 Å	22312	65·5	0·24	?0·01	77·0	0·5
4120-4010 Å	24540	160·6	1·125	..	128·4	0·1

     

F2Δr−A2Πi band system of CN

The spectrum of CN has been studied in condensed electrical discharge through flowing CH₃CN vapour. Ten new bands of F²?,?A²Π_i system in the region 2100–2700 Å are obtained. The vibrational constantsω ₀′ = 1229.7 cm.^?1 and ω₀′χ₀′= 14.0 cm.^?1 are obtained for the first time for the²Δ state of CN.     

Emission spectrum of bromine excited in the presence of argon

The wavelengths and wavenumbers of the band heads of the system 2660-2590 Å as obtained from the plates taken on the first order 21-feet grating spectrograph are given along with its vibrational analysis. This system is shown as the transition from an upper state at T _e =56776 cm.^?1 withω _e = 108·0 cm.^?1 to the³ Π _u (O _u ⁺) state at T _e =15918 cm.^?1 The lower state is the same as that of the two systems in the regions 2950-2670 Å and 3150-2970 Å reported earlier.     

Emission spectrum of bromine excited in the presence of argon

The wavelengths and wavenumbers of the band heads of the system 3150–2970 Å as obtained from the plates taken on the first order 21′ grating spectrograph are given along with the vibrational analysis. This system is shown to be due to a transition from an upper electronic state at T_e = 48516 cm.^-1 with ω′ _e = 162·0 cm.^?1 and ω′ _e χ′ _e = 0·29 cm.^?1 to the well-known³ Π _u (O _u ⁺) state at T_e = 15918 cm.^-1 This lower state is common with that of the system 2950–2670 Å.     

Rotational analysis of some of the bands of the orange system of FeO

The orange bands of FeO are excited in a low pressure arc in oxygen and photographed at dispersions of 0·8 and 0·5 Å/mm. respectively. Rotational analysis of five of the bands shows that they involve a¹ Σ-¹ Σ transition. The vibrational and rotational constants (in cm.^?1) of the upper and lowerΣ states are found to be

	Lower state	Upper state
B e	0·3491	0·3063
α e	0·0029	0·0032
w e	870·7	(ΔG½=770·0)
w e x e	4·39	..

     

The near ultraviolet absorption spectra ofortho- andmeta-thiocresols

The absorption spectra ofortho- andmeta-thiocresols have been studied in the present investigation. The ortho-thiocresol spectrum consists of about forty-five bands of rather a diffuse nature and in general low intensity in the region from 2873 Å to 2600 Å. The maximum number of bands is obtained by using a path length of 330 cm. for absorption, the temperature of the bulb being maintained at 14°C. Several of these bands are assigned as due tov-v-transitions. The (0, 0) band is chosen at 35386 cm.^?1 which is the strongest band on the longer wavelength side. Vibrational frequencies in the excited state have values 729, 957 and 1159 and combinations and overtones of these are present. Themeta-thiocresol spectrum consists of about forty bands of rather a diffuse nature and very weak intensities in the region from 2900 Å to 2590 Å. The maximum number of bands is obtained by using a path length 200 cm. for absorption and by keeping the temperature of the bulb at 20° C. The (0, 0) band is chosen to be that at 34793 cm.^?1 which is the strongest band on the longer wavelength side. Vibrational frequencies in the excited state have values 492, 611, 720, 845, 965, 1016 and 1155 cm.^?1 and combinations and overtones of these are present.     

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.     

Isotope shift studies of the ultra-violet and visible bands of P16O and P18O

The spectra of P¹⁶O and P¹⁸O were excited in sealed discharge tubes containing neon (2–3 mm. pressure), oxygen gas enriched to 65 per cent. of¹⁸O and trace amounts of phosphorus vapour and photographed on a 3 m. grating spectrograph at a dispersion of 2·5 Å/mm. Isotope shift studies in theβ-bands confirmed the earlier vibrational scheme of Curryet al. and showed conclusively that the red as well as the violet degraded bands belonged to the sameβ-system. The present studies of isotope shifts also confirmed the vibrational assignments of the extensive ultraviolet bands involving the² Σ ^??X² Π transition and theγ-bands (A² Σ ⁺?X² Π). In the case of the visible bands, they provided evidence for the first time that the bands at 5585 Å, 5962 Å and 6385 Å belonged to one system and involved 0–0, 0–1 and 0–2 transitions respectively.     

A new2 Π-X2 Π band system of NS

Vibrational and rotational analysis of some bands forming a new band system of NS is given. It is also shown that the system involves the ground X² Π _reg. state of the molecule, and is due to the transition² Π _reg.→X² Π _reg. The bands form a singlev″=0 progression withv′=7, 8, 9 and 10. The assignment of these quantum numbersv′, v″ is supported by (1) Δ₂F″ (J) values which are identical with those for thev″=0 bands of theβ andγ systems and (2) the isotopic shift data from¹⁵NS bands, respectively. The derived vibrational and rotational constants for the new² Π _reg. state are as follows (cm.^?1 units):

	T e	ω e	ω e x e	B e	D e
2 Π 3/2..	30364·8	803·3	3·82	0·6030	2·0×10?6
2 Π ½..	30292·3	797·0	3·63	0·5898	2·0×10?6

     

Rotational analysis of some bands of C1 Σ u + -X1 Σ g + system of P2 molecule involving lowν′,ν″ values

Ten ultraviolet bands of the C¹ Σ _u ⁺ -X¹ Σ _g ⁺ system of P₂ involving lowv′ andv″ values have been photographed at dispersion of 0·38 and 0·56 Å/mm. and analysed for their rotational structure. While four of these bands were analysed earlier, six of them,viz., 0–10, 1–12, 2–7, 2–14, 4–8 and 6–9 have been analysed for the first time during the present studies. The rotational constants, B _v S with lowv″ quantum numbers are obtained from which value of B _θ ^″ has been derived. The value of B _θ ^″ is found to be in agreement with the value obtained by Douglas and Rao from their study of A¹ Π _g-X¹ Σ _g ⁺ bands of P₂. Earlier findings on the perturbation ofν′=2 level of the C¹ Σ _u ⁺ state have been confirmed from the analysis of the 2–7, 2–14 and 2–15 bands. Theν ₀₀ values of the bands show large deviations from the expected values.     

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.     

Emission spectrum of bromine excited in the presence of argon—part I

Bromine was excited by an uncondensed transformer discharge in the presence of argon. The spectrum obtained was found to be different from what one gets without the presence of a foreign gas and consists of (1) a short discrete band system in the region 3150–2970 Å, (2) an extensive discrete band system in the region 2950–2670 Å, (3) a short and weak discrete system in the region 2660–2590 Å and a set of diffuse bands in the region 3340–3190 Å. The wavelengths and wave numbers of the band heads of the system 2950–2670 Å, as obtained from the measurements of the plates taken on the first order 21-ft. grating spectrograph, are given along with the vibrational analysis. This system is shown to be due to a transition from an upper electronic state at 51802 cm.^-1 with ω′_e = 150·5 cm.^-1 and ω′_e X′_e = 1·15 cm.^-1 to the well known³ II _α (O₂ ⁺) state at 15918 cm.^-1     

Quantization causes waves: Smooth finitely computable functions are affine

Every automaton (a letter-to-letter transducer) A whose both input and output alphabets are F _p = {0, 1,..., p - 1} produces a 1-Lipschitz map f _A from the space Z _p of p-adic integers to Z _p . The map fA can naturally be plotted in a unit real square I² ? R²: To an m-letter non-empty word v = γ _m-1γ _m-2... γ0 there corresponds a number 0.v ∈ R with base-p expansion 0.γ _m-1γ _m-2... γ0; so to every m-letter input word w = α _m-1α _m-2 ··· α0 of A and to the respective m-letter output word a(w) = β _m-1β _m-2 ··· β0 of A there corresponds a point (0.w; 0.a(w)) ∈ R². Denote P(A) a closure of the point set (0.w; 0.a(w)) where w ranges over all non-empty words.We prove that once some points of P(A) constitute a C ²-smooth curve in R², the curve is a segment of a straight line with a rational slope. Moreover, when identifying P(A) with a subset of a 2-dimensional torus T² ∈ R³, the smooth curves from P(A) constitute a collection of torus windings which can be ascribed to complex-valued functions ψ(x, t) = e ^i(Ax-2πBt) (x, t ∈ R), i.e., to matter waves. As automata are causal discrete systems, the main result may serve a mathematical reasoning why wave phenomena are inherent in quantum systems: This is just because of causality principle and discreteness of matter.     

On real solutions of systems of equations

Systems of equations f ₁ = ··· = f _n?1 = 0 in ? ⁿ = {x} having the solution x = 0 are considered under the assumption that the quasi-homogeneous truncations of the smooth functions f ₁,..., f _n?1 are independent at x ≠ 0. It is shown that, for n ≠ 2 and n ≠ 4, such a system has a smooth solution which passes through x = 0 and has nonzero Maclaurin series.     

Characteristics ofπ −-nucleon collisions at a primary energy of 4·4 GeV

Eight hundred and sixteen nuclear interactions produced by 4·4 GeVπ ^?-mesons in nuclear emulsion have been obtained by “along the track” scanning procedure. Favourable secondary particles from a selected 290π ^?-N (pion-nucleon) collisions have been identified by blob-density and multiple scattering measurements. It is found that the pion often persists in theseπ ^?-N collisions, the average persistence is estimated to be 0·24 per collision. It is estimated thatπ-N andπ-π collisions account for 60% and 28% respectively of the secondary particles. The average number of charged shower particles is 〈n _s〉=2·09±0·12, the average number of created charged particles is 〈n _e±〉=1·94±0·12, the average number of protons with energy greater than 300 MeV is 〈n _p〉=0·15±0·05 and the average number of charged kaons is found to be 〈n _k±〉=0·11±0·06. The integral energy spectra of pions in C-system as well as in L-system are well represented by exponential forms. The average inelasticity of the proton in C-system is found to be 0·52±0·10. The charge retention probability for protons inπ ^?-p collisions is 0·45±0·07.     

Ranks of matrices with few distinct entries

It is consistent that P(ω ₁) is the union of less than \({2^{{\aleph _1}}}\) parts such that if A ₀,..., A _n?1, B ₀,..., B _m?1 are distinct elements of the same part, then |A ₀ ∩ · · · ∩ A _n?1 ∩ (ω ₁ ? B ₀) ∩ · · ·∩ (ω ₁ ? B _m?1)| = N₁.     

The spectrum of iodine excited in the presence of argon

The band systems of iodine in the regions 3455-3015 Å, 2785-2750 Å and 2730-2520 Å obtained by earlier workers using prism spectrographs are now photographed in the first and second orders of a 21-ft. grating spectrograph. A large number of new bands are obtained in all these three systems which are now extended to the regions 3461-3015 Å, 2785-2731 Å and 2729-2486 Å. The wavelengths and wavenumbers of all the bands are recorded along with their visually estimated intensities. The Deslandres schemes for the three systems representing all the bands are given and are found to be supported by the corresponding intensity distributions of the expected type. It was found that the two systems 3460-3015 Å and 2785-2731 Å do not involve for their lower levels the ground state as assumed by the earlier workers but the³Π_u (O _u ⁺) state at 15642 cm.^?1, which is also the lower state for the 4420-4000 Å system. The band system in the region 2730-2486 Å has for its lower level the ground state of the molecule as reported by the earlier workers. A reanalysis of this system made to include all the bands observed in the present experiments, gave vibrational constants slightly different from those obtained by earlier workers. The vibrational constants of the upper states of the four different systems that one gets by exciting iodine in the presence of argon are

System	Te	ωe	ωeXe	ωeYe
4400-4000Å	41411 cm.-1	102·2 cm.-1	0·34 cm.-1	..
3460-3015Å	45937 cm.-1	103·7 cm.-1	0·95 cm.-1	..
2785-2731Å	51847 cm.-1	112·4 cm.-1	0·711 cm.-1	0·004 cm.-1
2730-2486Å	47207 cm.-1	96·5 cm.-1	0·510 cm.-1	0·0033 cm.-1

     

Word maps and word maps with constants of simple algebraic groups

In the present paper, we consider word maps w: G ^m → G and word maps with constants w _Σ: G ^m → G of a simple algebraic group G, where w is a nontrivial word in the free group F _m of rank m, w _Σ = w ₁ σ ₁ w ₂ ··· w _r σ _r w _{r + 1}, w ₁, …, w _{r + 1} ∈ F _m , w ₂, …, w _r ≠ 1, Σ = {σ ₁, …, σ _r | σ _i ∈ G Z(G)}. We present results on the images of such maps, in particular, we prove a theorem on the dominance of “general” word maps with constants, which can be viewed as an analogue of a well-known theorem of Borel on the dominance of genuine word maps. Besides, we establish a relationship between the existence of unipotents in the image of a word map and the structure of the representation variety R(Γ_w, G) of the group Γ_w = F _m /<w>.     

The near ultraviolet absorption spectrum ofpara-thio-cresol

The absorption spectrum ofpara-thio-cresol consists of about ten bands in the region 2922 to 2600 Å. The bands are quite intense but broad and fail to show any structure such as is observed in the case ofpara-cresol bands. The maximum number of bands about ten is obtained by using an absorption path length of 100 cm. The (0, 0) band is chosen to be that at 34222 cm.^?1 which is the strongest band on the longer wavelength side. Vibrational frequencies in the excited state have values 353, 752 and 1114 and combinations and overtones of these are found to be present.