A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.

     

Pressure dependence of the compressibility of alkali halides

The parameterC ₁=[(1/K _T )/P] _T , which describes the pressure variation of the compressibility, has been examined correlating the thermodynamical and interatomic potential approaches employing fewer approximations than has been usual heretofore. General expressions have been derived forC ₁ by including the thermal correction terms, which have generally been ignored in previous studies concerning thermal properties of ionic crystals. The parameterC ₁ has also been related to the Grüneisen parameter, , using a relation given earlier. The applicability of the derived equations is investigated and discussed for alkali halides employing few realistic potential forms. A good general accord is found with the available experimental data, which exhibits an essential improvement over other theoretical determinations.     

Transition metal chemistry of oxime-containing ligands,VI: magnetic and structural properties of mono (pyridine-2-aldoxime) dithiocyanato iron (II) and mono (6-methylpyridine-2-aldoxime) dithiocyanato iron (II) complexes

The complexes of pyridine-2-aldoxime (HPOX) and 6-methylpyridine-2-aldoxime (HMPX) with iron (II) thiocyanate of the type [Fe(L)(NCS)₂] (L=HPOX and HMPX) have been prepared and characterized. A study of X-ray, magnetic, vibrational spectra (conventional and far-infrared), electronic spectra andMössbauer spectra has indicated that these complexes have polymeric, pseudo octahedral, coordination geometry with linear bridging thiocyanate ligands. The electronic spectra of mono complexes show a larger, low symmetry, ligand field than that present in [Fe(L)₂(NCS)₂] complexes. UnperturbedMössbauer spectra show a large quadrupole splitting, E _Q, and smaller isomer shift values in these iron (II) thiocyanate complexes. The magnetically perturbedMössbauer spectra of these iron(II) thiocyanate complexes at room temperature show that the principal component of the electric field gradient tensor is positive and corresponds to ad _xy (⁵B₂) ground state.With 2 Figures     

Nucleophilic Substitution on 5-Nitrobenzofurazan-3-Oxide: A New Synthetic Route for Novel Benzofurazan-5, 5′-Oxybis 3, 3′-Dioxide and Benzofurazan-5, 5′-Thiobis-3, 3′-Dioxide

The nucleophilic substitution of the nitro group in 5-nitrobenzofurazan-3-oxide is studied undder soild-liquid phase-transfer catalysis (PTC) conditions.     

Topochemical models for anti-HIV activity of 1-alkoxy-5-alkyl-6-(arylthio)uracils

Relationship between topochemical indices and anti-HIV-1 (HTLV-III) inhibitory activity of 1-alkoxy-5-alkyl-6-(arylthio)uracils has been studied. Superadjacency, an adjacency-cum-distance-based, topochemical index and Wiener’s, a distance-based, topochemical index were calculated for a set of 36 1-alkoxy-5-alkyl-6-(arylthio)uracils. Resulting data were analyzed and suitable models were developed after identification of the active ranges. Subsequently, a biological activity was assigned to each of the compounds using these models and compared with the reported anti-HIV-1 activity. High accuracy of prediction was observed using these models. Statistical analysis revealed significance of the proposed models as well as a lack of correlation between the topochemical indices employed for the chosen data set.     

One-pot three-component 1,3-dipolar cycloaddition of azomethineylides to nitrofuran containing acetylenic ketones and molecular docking studies of the cycloadducts

One-pot three-component 1,3-dipolar cycloaddition reaction of azomethineylides generated from various combinations of isatin and ninhydrin with α-aminoacids to 5-nitrofurancontaining acetylenic ketones was carried out under thermal and microwave methods. The study of the regiochemical trend during the cycloaddition suggested that the nitrofuran ring exert no effect on the regiochemistry of the reaction as observed in the case of nitrofuran containing chalcones. The reason for the nil influence of the nitrofuran group is attributed to the increased electron density due to the triple bond. The newly synthesized compounds were docked to the active site of human anaplastic lymphoma kinase (ALK) to know the cancer cell toxicity in silico. The compounds 4b and 5a showed good binding interactions with the target in the active site.     

Encryption and decryption using a sandwich phase diffuser made by using two speckle patterns and placed in the Fourier plane: Simulation results

In the present paper, we describe the encryption and decryption of two-dimensional images. The encryption is done by employing a sandwich phase diffuser made by using two elongated speckle patterns, and placed in the Fourier plane of a double random phase encoding system. After encryption, the two constituent phase diffusers of such a sandwich diffuser are separated. During decryption, if the conjugate of either of the two elongated phase speckle patterns is used, the image cannot be retrieved. Correct decryption is also not possible if a sandwich diffuser with any of the phase speckle patterns is shifted in position with respect to the other. For decryption, the encrypted image is Fourier transformed and multiplied by the conjugate of the sandwich diffuser, and then the product is further Fourier transformed. It is possible to generate the image only if both the elongated phase speckle patterns are matched point-to-point and then the proper conjugate is made. The use of elongated speckle patterns in constituting a sandwich phase diffuser makes the system less complicated as compared to the use of a sandwich diffuser made with normal speckle patterns, enabling an easy alignment of the random phase diffuser at the time of rejoining the constituent diffusers for making the right key. The ease of alignment is due to the reduction of the requirement of 360° scanning at the time of rejoining these diffusers with little reduction in the security of the system. Simulation results are presented in support of the proposed idea. For optical implementation, the decrypted image may be obtained by generating a phase conjugate wave by the phase conjugation technique, and passing through the same sandwich phase diffuser. To evaluate the reliability of the technique, mean square error (MSE) between the decrypted and original image has been calculated.     

Weak invariance of the multidimensional rank statistic for nonstationary absolutely regular processes

In this paper, we study the weak invariance of the multidimensional rank statistic when the underlying random variables are nonstationary absolutely regular.