Acyclic Edge Coloring of Graphs with Maximum Degree 4

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). It was conjectured by Alon, Sudakov, and Zaks that for any simple and finite graph G, a'(G) <= Delta+2, where Delta=Delta(G) denotes the maximum degree of G. We prove the conjecture for connected graphs with Delta(G)<= 4, with the additional restriction that m <= 2n-1, where n is the number of vertices and m is the number of edges in G. Note that for any graph G, m <= 2n, when Delta(G)<= 4. It follows that for any graph G if Delta(G)<= 4, then a'(G) <= 7.

Structure and Conformation of an Antidepressant Drug, Nitroxazepine Hydrochloride Monohydrate

CIsH20N3Oa+.C1-.H2 O, M r = 395, orthorhombic, Pn21a, a = 7.710 (4), b = 11.455 (3), c -- 21.199 (3)/k, Z = 4, V = 1872.4/k 3, D m = 1.38, D C = 1.403 g cm -3, F(000) = 832, g(Cu Kct) = 20.94 cm -l. Intensities for 1641 reflections were measured on a Nonius CAD-4 diffractometer; of these, 1470 were significant. The structure was solved by direct methods and refined to an R index of 0.045 using a blockdiagonal least-squares procedure. The angle between the least-squares planes through the benzene rings is 125.0 (5) ° and the side chain is folded similarly to one of the independent molecules of imipramine hydrochloride.

Structure and conformation of an anti-depressant drug, nitroxazepine hydrochloride monohydrate

CIsH20N3Oa+.C1-.H2 O, M r = 395, orthorhombic, Pn21a, a = 7.710 (4), b = 11.455 (3), c -- 21.199 (3)/k, Z = 4, V = 1872.4/k 3, D m = 1.38, D C = 1.403 g cm -3, F(000) = 832, g(Cu Kct) = 20.94 cm -l. Intensities for 1641 reflections were measured on a Nonius CAD-4 diffractometer; of these, 1470 were significant. The structure was solved by direct methods and refined to an R index of 0.045 using a blockdiagonal least-squares procedure. The angle between the least-squares planes through the benzene rings is 125.0 (5) ° and the side chain is folded similarly to one of the independent molecules of imipramine hydrochloride.

Refractive index measurement by the moire technique

A simple moire method for the direct measurement of refractive indices is presented. The change of magnification and/or distortion of the image of a linear grating when viewed through a refractive index field is amplified by means of moire fringes and is measured directly. Relations between the index of refraction and fringe spacing are derived and have been verified experimentally.

Termination of pregnancy in macaques (Macaca radiata) using monkey antiserum to ovine luteinizing hormone

The ability of a monkey antiserum to ovine LH to interrupt gestation in monkeys has been established. The antiserum has been shown to neutralize monkey pituitary LH by a number of criteria. The significant increase in serum progesterone level on day 23 of the cycle shown by mated monkeys has been used as an index of pregnancy. Injection of LH antiserum during the first week of missed menses (day 29–31 of cycle or day 18–20 of gestation) causes significant reduction in serum levels of progesterone followed by onset of bleeding which is interpreted as the termination of gestation. The same dose of non-immune serum given to monkeys during the same period does not have any deleterious effect on the progress of pregnancy. The antiserum-treated animals after the termination of gestation, resume cyclicity. Injection of antiserum after day 25 of gestation does not bring about termination of pregnancy. It is suggested that by using antisera raised in humans to ovine LH, this method may be developed as a fertility control measure in humans.

Crystal structure and conformation of the cyclic dipeptide cyclo-(L-histidyl-L-aspartyl) trihydrate

The crystal structure of cyclo-(L-histidyl-L-aspartyl) trihydrate has been determined by x-ray diffraction techniques, and refined to a final R index of 0.056 for 1601 reflections. The molecule is in a folded conformation, with the imidazole ring facing the diketopiperazine ring. However, since the diketopiperazine ring is essentially planar, the interaction between the two rings is not as intimate as in those cyclic dipeptides in which the diketopiperazine ring is in a boat conformation with the side chain occupying an axial, or flagpole, site. Planarity of the diketopiperazine ring may be dictated by steric interactions between the imidazole ring and the aspartyl side chain. The molecule is a zwitterion, a proton having been transferred from the carboxyl group of the aspartyl side chain to the imidazole ring.

Acyclic edge coloring of subcubic graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and it is denoted by a′(G). From a result of Burnstein it follows that all subcubic graphs are acyclically edge colorable using five colors. This result is tight since there are 3-regular graphs which require five colors. In this paper we prove that any non-regular connected graph of maximum degree 3 is acyclically edge colorable using at most four colors. This result is tight since all edge maximal non-regular connected graphs of maximum degree 3 require four colors.

Biotransformation of cholesterol to diosgenin by freely suspended and immobilised cells of Dioscorea bulbifera L.

The cell suspension cultures, established from the friable callus which was risen from the nodal segments of Dioscorea bulbifera L. in Murashige-Skoog (MS) medium supplemented with indole-3-butryic acid (20 mg L- 1), was examined for cell growth in MS medium fed with cholesterol (50 mg L- 1 and 100 mg L- 1) after 8, 10, 12, 14, 16, and 18 days of culture. The growth index of the cell suspension culture on the 8th day was 1.2 and gradually inclined to 1.9 on the 16th day and remained the same at the 18th day. There is no marked difference in the cell growth of cholesterol-treated and control cell suspension culture. The maximum accumulation of diosgenin was noticed on the 14th day in control and cholesterol-treated cell suspension culture and immobilised cell cultures. The highest concentration of diosgenin, 2.94% and 2.14% dry weight, was obtained in immobilised cell culture and cell suspension culture treated with 100 mg L- 1 cholesterol, respectively.

Design and analysis of ARROW-based racetrack resonator vibration sensor for inertial navigation application

In this paper we propose and analyze a novel racetrack resonator based vibration sensor for inertial grade application. The resonator is formed with an Anti Resonance Reflecting Optical Waveguide (ARROW) structure which offers the advantage of low loss and single mode propagation. The waveguide is designed to operate at 1310nm and TM mode of propagation since the Photo-elastic co-efficient is larger than TE mode in a SiO2/ Si3N4/ SiO2. The longer side of the resonator is placed over a cantilever beam with a proof mass. A single bus waveguide is coupled to the resonator structure. When the beam vibrates the resonator arm at the foot of the cantilever experiences maximum stress. Due to opto-mechanical coupling the effective refractive index of the resonator changes hence the resonance wavelength shifts. The non uniform cantilever beam has a dimension of 1.75mm X 0.45mm X 0.020mm and the proof mass has a dimension of 3mm X 3mm X 0.380mm. The proof mass lowers the natural frequency of vibration to 410Hz, hence designed for inertial navigation application. The operating band of frequency is from DC to 100Hz and acceleration of less than 1g. The resonator has a Free Spectral Range (FSR) of 893pm and produces a phase change of 22.4mrad/g.

Influence of surfactant and annealing temperature on optical properties of sol-gel derived nano-crystalline TiO2 thin films

Titanium dioxide thin films have been synthesized by sol-gel spin coating technique on glass and silicon substrates with and without surfactant polyethylene glycol (PEG). XRD and SEM results confirm the presence of nano-crystalline (anatase) phase at an annealing temperature of 300 degrees C. The influence of surfactant and annealing temperature on optical properties of TiO2 thin films has been studied. Optical constants and film thickness were estimated by Swanepoel's (envelope) method and by ellipsometric measurements in the visible spectral range. The optical transmittance and reflectance were found to decrease with an increase in PEG percentage. Refractive index of the films decreased and film thickness increased with the increase in percentage of surfactant. The refractive index of the un-doped TiO2 films was estimated at different annealing temperatures and it has increased with the increasing annealing temperature. The optical band gap of pure TiO2 films was estimated by Tauc's method at different annealing temperature. (C) 2010 Elsevier B.V. All rights reserved.

Crystal chemistry of a new solid solution in the BaO-Bi2O3-Nb2O5 system: Ba-5x/2-Bi(1-x)5/3Nb5O15

A solid solution of the type Ba5x/2Bi(1-x)5/3Nb5O15 has been identified in the BaO-Bi2O3-Nb2O5 system for the first time. The limits of the solid solution are within the range 0.52 <= x <= 0.80. The compositions x = 0.52, 0.60, 0.72, 0.77, 0.78, and 0.80 were synthesized by the solid-state technique from the starting materials in stoichiometric quantities. The powder X-ray patterns of all the phases in the domain indicate a structural similarity to tetragonal tungsten bronzes (TTBs). The compositions below x = 0.52 and those above x = 0.80 exhibit barium niobate and bismuth niobate impurities, respectively. Single crystals of the composition x = 0.77 were obtained by the melt cooling technique. The crystal structure of Ba3.85/2Bi1.15/3Nb5O15 (x = 0.77) was solved in the tetragonal space group P4bm (No. 100) with a = 12.4938 (14) angstrom, c = 3.9519 (2) A, V = 616.87 (10) angstrom(3), and Z = 2 and was refined to an R index of 0.034. Dielectric measurements on all the phases indicate a typical relaxor behavior with a broad phase transition at T-m approximate to 300 K.

Crystal structure and ionic conductivity of a new bismuth tungstate,Bi3W2O10.5

The compound Bi3W2O10.5 was synthesized by the solid-state technique from Bi2O3 and WO3 in stoichiometric quantities. Single crystals were grown by the melt-cooling technique and the crystal structure was solved in the tetragonal 141in space group with a = 3.839 (1) A, c = 16-3S2 (5) A, V = 241.4 (1) angstrom(3), Z = 4 and was refined to an R index of 0.0672. The structure represents a modification of the Aurivillius phase and consists of [Bi2O2](2+) units separated by WO8 polyhedra. a.c. impedance studies indicate oxide ion conductivity of 2.91 10(-5) cm(-1) at 600 degrees C.

Retrieval of dust aerosols during night: improved assessment of long wave dust radiative forcing over Afro-Asian regions

Several investigators in the past have used the radiance depression (with respect to clear-sky infrared radiance), resulting from the presence of mineral dust aerosols in the atmosphere, as an index of dust aerosol load in the atmosphere during local noon. Here, we have used a modified approach to retrieve dust index during night since assessment of diurnal average infrared dust forcing essentially requires information on dust aerosols during night. For this purpose, we used infrared radiance (10.5-12.5 mu m), acquired from the METEOSAT-5 satellite (similar to 5 km resolution). We found that the `dust index' algorithm, valid for daytime, will no longer hold during the night because dust is then hotter than the theoretical dust-free reference. Hence we followed a `minimum reference' approach instead of a conventional `maximum reference' approach. A detailed analysis suggests that the maximum dust load occurs during the daytime. Over the desert regions of India and Africa, maximum change in dust load is as much as a factor of four between day and night and factor of two variations are commonly observed. By realizing the consequent impact on long wave dust forcing, sensitivity studies were carried out, which indicate that utilizing day time data for estimating the diurnally averaged long-wave dust radiative forcing results in significant errors (as much as 50 to 70%). Annually and regionally averaged long wave dust radiative forcing (which account for the diurnal variation of dust) at the top of the atmosphere over Afro-Asian region is 2.6 +/- 1.8 W m(-2), which is 30 to 50% lower than those reported earlier. Our studies indicate that neglecting diurnal variation of dust while assessing its radiative impact leads to an overestimation of dust radiative forcing, which in turn result in underestimation of the radiative impact of anthropogenic aerosols.

Studies on follicular growth in the immature rat and hamster: Effect of a single injection of gonadotropin or estrogen on the rate of3H-thymidine incorporation into ovarian DNAin vitro

Initiation of follicular growth by specific hormonal stimuli in ovaries of immature rats and hamsters was studied by determining the rate of incorporation of3H-thymidine into ovarian DNAin vitro. Incorporation was considered as an index of DNA synthesis and cell multiplication. A single injection of pregnant mare serum gonadotropin could thus maximally stimulate by 18 hr3H-thymidine incorporation into DNA of the ovary of immature hamsters. Neutralization of pregnant mare serum gonadotropin by an antiserum to ovine follicle stimulating hormone only during the initial 8–10 hr and not later could inhibit the increase in3H-thymidine incorporationin vitro observed at 18 hr, suggesting that the continued presence of gonadotropin stimulus was not necessary for this response. The other indices of follicular growth monitored such as ovarian weight, serum estradiol and uterine weight showed discernible increase at periods only after the above initial event. A single injection of estrogen (diethyl stilbesterol or estradiol-l7β) could similarly cause 18 hr later, a stimulation in the rate of incorporation of3H-thymidine into DNAin vitro in ovaries of immature rats. The presence of endogenous gonadotropins, however, was obligatory for observing this response to estrogen. Evidence in support of the above was two-fold: (i) administration of antiserum to follicle stimulating hormone or luteinizing hormone along with estrogen completely inhibited the increase in3H-thymidine incorporation into ovarian DNAin vitro; (ii) a radioimmunological measurement revealed following estrogen treatment, the presence of a higher concentration of endogenous follicle stimulating hormone in the ovary. Finally, administration of varying doses of ovine follicle stimulating hormone along with a constant dose of estrogen to immature rats produced a dose-dependent increment in the incorporation of3H-thymidine into ovarian DNAin vitro. These observations suggested the potentiality of this system for developing a sensitive bioassay for follicle stimulating hormone.

Terahertz Time Domain Spectroscopy to Detect Low-Frequency Vibrations of Double-Walled Carbon Nanotubes

We have measured the frequency-dependent real index of refraction and extinction coefficient (and hence the complex dielectric function) of a free-standing double-walled carbon nanotube film of thickness 200 nm by using terahertz time domain spectroscopy in the frequency range 0.1 to 2.5 THz. The real index of refraction and extinction coefficient have very high values of approximately 52 and 35, respectively, at 0.1 THz, which decrease at higher frequencies. Two low-frequency phonon modes of the carbon nanotubes at 0.45 and 0.75 THz were clearly observed for the first time in the real and imaginary parts of the complex dielectric function along with a broad resonance centred at around 1.45 THz, the latter being similar to that in single-walled carbon nanotubes assigned to electronic excitations. Our experiments bring out a possible application of double-walled carbon nanotube films as a neutral density filter in the THz range.