The decay of Ho and Ho

The disintegration characteristics of ^164mHo and ^164gHo have been studied using a high-resolution Ge(Li) spectrometer. Radioactive samples of ^164mHo and ^164gHo were obtained through the (n, 2n) reaction on spectroscopically pure holmium oxide with 14 MeV neutrons. The isomeric cross-section ratio for the yields of the ground and metastable states has been estimated to be 1.0±0.25. Gamma rays of 37.7 and 56.1 keV energy have been assigned to the decay of ^164mHo and 73.4 and 91.5 keV γ-rays are attributed to the decay of ^164gHo by electron capture and negaton emission, respectively. The branching ratio for the electron capture decay of ^164gHo to the levels in ¹⁶⁴Dy has been estimated accurately from the analysis of X-ray intensities. The results have been incorporated into a decay scheme.     

Poisson-Jacobi transforms

The solutions of the Jacobi difference heat equation ▽ _n v(n, t)=(δ/δt)v (n, t) are considered. The theory of Poisson-Jacobi transform is developed to solve the equation. Convergence and inversion theorems are established.

     

Some problems and conjectures in number theory

In this article, we shall discuss some interesting, viable, meaningful, applicable and productive conjectures and methods to deal with some fundamental results in the theory of numbers.     

Geometrical solution of some cubic equations with non-real roots

A general cubic equation ax ³ + bx ² + cx + d = 0 where a, b, c, d ∈R, a ≠ 0 has three roots with two possibilities—either all three roots are real or one root is real and the remaining two roots are imaginary. Dealing with the second possibility this paper attempts to give the geometrical locations of the imaginary roots of the equation under three different sets of conditions. These sets of conditions include: (i) the real root of the given cubic equation is given, (ii) the real part of an imaginary root is given, and (iii) the imaginary part of an imaginary root is given.     

A short Proof of Bezout's Theorem in P2

We will give a new short proof of Bezout's Theorem for complex algebraic curves in P ² which is local.     

New insights into the visible-light-induced DNA cleavage activity of dipyridoquinoxaline complexes of bivalent 3d-metal ions

Dipyridoquinoxaline (dpq) complexes of bivalent 3d-metal ions, viz., [FeII(dpq)3](PF6)2 (1), [CoII(dpq)3](ClO4)2 (2), [NiII(dpq)3](ClO4)2 (3), [CuII(dpq)2(H2O)](ClO4)2 (4), [ZnII(dpq)3](ClO4)2 (5), and [ZnII(dpq)2(DMF)2](ClO4)2 (5a) (DMF = N,N-dimethylformamide), are prepared and their photoinduced DNA cleavage activity studied. Structural characterization for the complexes 1 and 5a is done by single-crystal X-ray crystallography. All the complexes show efficient binding propensity to calf thymus DNA with a binding constant (K) value of approximately 10(5) M(-1). Complexes 1, 2, and 4 show metal-based cyclic voltammetric responses at 1.2, 0.4, and 0.09 V (vs SCE) in DMF 0.1 M [Bun4N](ClO4) assignable to the respective FeIII/FeII, CoIII/CoII, and CuII/CuI couples. The NiII and ZnII complexes do not show any metal-based redox process. The dpq-based reductions are observed in the potential range of -1.0 to -1.7 V vs SCE. DNA melting and viscosity data indicate the groove-binding nature of the complexes. Control experiments using distamycin-A suggest a minor groove-binding propensity of the complexes. The complexes exhibit photoinduced cleavage of supercoiled pUC19 DNA in UV light of 365 nm. The diamagnetic d6-FeII and d10-ZnII complexes are cleavage-inactive on irradiation with visible light. The paramagnetic d7-CoII and d9-CuII complexes exhibit efficient DNA cleavage activity on photoirradiation at their respective d-d band. The paramagnetic d8-NiII complex displays only minor DNA cleavage activity on irradiation at its d-d band. The DNA cleavage reactions at visible light under aerobic conditions involve the formation of hydroxyl radical. The CoII complex shows photocleavage of DNA under an argon atmosphere. Theoretical calculations on the complexes suggest a photoredox pathway in preference to a type-2 process forming singlet oxygen for the visible-light-induced DNA cleavage activity of the 3d-metal complexes. The theoretical data also predict that the photoredox pathway is favorable for the 3d7-CoII and 3d9-CuII complexes to exhibit DNA cleavage activity, while the analogous 3d6-FeII and 3d8-NiII complexes are energetically unfavorable for the exhibition of such activity under visible light. The CoII and CuII complexes are better suited for designing and developing new metal-based PDT agents than their cleavage-inactive FeII, NiII, and ZnII analogues.     

Structure, energy, and IR spectra of I2*-.nH2O clusters (n=1-8): a theoretical study

The authors report theoretical results on structure, bonding, energy, and infrared spectra of iodine dimer radical anion hydrated clusters, I(2) (-).nH(2)O (n=1-8), based on a systematic study following density functional theory. Several initial guess structures are considered for each size cluster to locate minimum energy conformers with a Gaussian 6-311++G(d,p) split valence basis function (triple split valence 6-311 basis set is applied for iodine). It is observed that three different types of hydrogen bonded structures, namely, symmetrical double hydrogen bonding, single hydrogen bonding, and interwater hydrogen bonding structures, are possible in these hydrated clusters. But conformers having interwater hydrogen bonding arrangements are more stable compared to those of double or single hydrogen bonded structures. It is also noticed that up to four solvent H(2)O units can reside around the solute in interwater hydrogen bonding network. At the maximum six H(2)O units are independently linked to the dimer anion having four double hydrogen bonding and two single hydrogen bonding, suggesting the hydration number of I(2) (-) to be 6. However, conformers having H(2)O units independently linked to the iodine dimer anion are not the most stable structures. In all these hydrated clusters, the odd electron is found to be localized over two I atoms and the two atoms are bound by a three-electron hemi bond. The solvation, interaction, and vertical detachment energies are calculated for all I(2) (-).nH(2)O clusters. Energy of interaction and vertical detachment energy profiles show stepwise saturation, indicating geometrical shell closing in the hydrated clusters, but solvation energy profile fails to show such behavior. A linear correlation is observed between the calculated energy of interaction and vertical detachment energy. It is observed that formation of I(2) (-)-water cluster induces significant shifts from the normal O-H stretching modes of isolated H(2)O. However, bending mode of H(2)O remains insensitive to the successive addition of solvent H(2)O units. Weighted average energy profiles and IR spectra are reported for all the hydrated clusters based on the statistical population of individual conformers at room temperature.     

Structure and photoelectron spectral properties of I(-)·nCO2 clusters: an ab initio study

Structures and photoelectron spectral properties of I^??nCO₂ (n=1–7) clusters are presented at the level of second‐order Møller–Plesset perturbation theory with relativistic corrections. Triple split‐valence 6‐311++G(d,p) basis set functions are employed herein. It is observed that the CO₂ molecules approach the I^? anion from one side in all the clusters and that I^??nCO₂ clusters prefer the surface structure. The calculated vertical detachment energy of these clusters is in excellent agreement with the reported experimentally measured values (within 4 %). Efforts are also made to extract vertical detachment energy of large size of clusters, including the bulk. The extracted vertical detachment energy values for larger clusters (n=8–13) by employing the microscopic theory‐based expression are also close (within 4 %) to that of the experimentally measured values.