Sampling with a String

Kramer's sampling theorem forms a bridge between the Whittaker-Shannon-Kotel'nikov sampling theorem and boundary-value problems. It has been shown that sampling expansions associated with Sturm-Liouville boundary-value problems are Lagrange-type sampling series, i.e., Lagrange series with infinitely many terms converging to entire functions. String theory as developed by Feller, Kac, and Krein, is a generalization of the Sturm-Liouville theory. We investigate sampling series associated with strings and compare them with those associated with Sturm-Liouville problems. We show that unlike sampling series associated with Sturm-Liouville problems, those associated with strings include not only Lagrange-type sampling series, but also Lagrange polynomial interpolation.     

On f-injective modules

In this paper, the notions of f-injective and f^*-injective modules are introduced. Elementary properties of these modules are given. For instance, a ring R is coherent iff any ultraproduct of f-injective modules is absolutely pure. We prove that the class S^* \Sigma^* of f^*-injective modules is closed under ultraproducts. On the other hand, S^* \Sigma^* is not axiomatisable. For coherent rings R, S^* \Sigma^* is axiomatisable iff every c₀ \chi_0 -injective module is f^*-injective. Further, it is shown that the class S \Sigma of f-injective modules is axiomatisable iff R is coherent and every c₀ \chi_0 -injective module is f-injective. Finally, an f-injective module H, such that every module embeds in an ultraprower of H, is given.     

A Generalized Sampling Theorem with the Inverse of an Arbitrary Square Summable Sequence as Sampling Points

In this article a generalized sampling theorem using an arbitrary sequence of sampling points is derived. The sampling theorem is a Kramer-type sampling theorem, but unlike Kramer's theorem the sampling points are not necessarily eigenvalues of some boundary value problems. The theorem is then used to characterize a class of entire functions that can be reconstructed from their sample values at the points t_n = an + b if n = 0, 1, 2, ... and t_n = an + c if n = 0, -1, -2, ..., where a, b, c are arbitrary constants. The reconstruction formula is derived explicitly in the form of a sampling series expansion. When a = 1, b = 0 = c, the famous Whittaker-Shannon-Kotel'nikov sampling theorem is obtained as a special case.     

Indecomposable modules over right pure semisimple rings

The aim of this paper is to prove the following result. IfA is a right pure semisimple ring, then it satisfies one of the two following statements:

1. For any positive integern, there are at most finitely many indecomposable right modules of lengthn; or
2. There is an infinite number of integersd such that, for eachd, A has infinitely many indecomposable right modules of lengthd.

The result is derived with the aid of ultraproduct-technique.     

Investigation of diazepam drug using thermal analyses, mass spectrometry and semi-empirical MO calculation

In the present work diazepam (Dz) drug was investigated using thermal analyses (TA) measurements (TG/DTG) in comparison with EI mass spectral (MS) fragmentation at 70 and 20 eV. Semi-empirical MO calculations, MNDO procedure, have been carried out on diazepam both as neutral molecule and the corresponding positively charged molecular ion. These include molecular geometry, bond order, charge distribution, heats of formation and ionization energy. Thermogravimetric and kinetic analysis, reveal a high response of the drug to the temperature variation with very fast rate. It is completely decomposed in the temperature range between 204 and 340 degrees C with average kinetic energy (KE) at 164.69 kJ mol(-1). On the other hand, diazepam can easily fragmented at low energy after ionization by electron energy at 9.56 eV. The losses of CO gas molecules followed by chlorine gas from the entity of diazepam (both neutral and charged molecular ion) as the best selected pathway were observed in both mass spectra (MS) and thermal analyses (TA). MNDO calculation was applied to declare both TA and MS observations.     

Deciphering the Role of Filamin B Calponin-Homology Domain in Causing the Larsen Syndrome,Boomerang Dysplasia,and Atelosteogenesis Type I Spectrum Disorders via a Computational Approach

Filamins (FLN) are a family of actin-binding proteins involved in regulating the cytoskeleton and signaling phenomenon by developing a network with F-actin and FLN-binding partners. The FLN family comprises three conserved isoforms in mammals: FLNA, FLNB, and FLNC. FLNB is a multidomain monomer protein with domains containing an actin-binding N-terminal domain (ABD 1–242), encompassing two calponin-homology domains (assigned CH1 and CH2). Primary variants in FLNB mostly occur in the domain (CH2) and surrounding the hinge-1 region. The four autosomal dominant disorders that are associated with FLNB variants are Larsen syndrome, atelosteogenesis type I (AOI), atelosteogenesis type III (AOIII), and boomerang dysplasia (BD). Despite the intense clustering of FLNB variants contributing to the LS-AO-BD disorders, the genotype-phenotype correlation is still enigmatic. In silico prediction tools and molecular dynamics simulation (MDS) approaches have offered the potential for variant classification and pathogenicity predictions. We retrieved 285 FLNB missense variants from the UniProt, ClinVar, and HGMD databases in the current study. Of these, five and 39 variants were located in the CH1 and CH2 domains, respectively. These variants were subjected to various pathogenicity and stability prediction tools, evolutionary and conservation analyses, and biophysical and physicochemical properties analyses. Molecular dynamics simulation (MDS) was performed on the three candidate variants in the CH2 domain (W148R, F161C, and L171R) that were predicted to be the most pathogenic. The MDS analysis results showed that these three variants are highly compact compared to the native protein, suggesting that they could affect the protein on the structural and functional levels. The computational approach demonstrates the differences between the FLNB mutants and the wild type in a structural and functional context. Our findings expand our knowledge on the genotype-phenotype correlation in FLNB-related LS-AO-BD disorders on the molecular level, which may pave the way for optimizing drug therapy by integrating precision medicine.     

Dithiocarbamates as Precursors in Organic Chemistry; Synthesis and Uses

Abstract

Organic dithiocarbamates have received great attention due to their interesting chemistry and wide utility as radical precursors and intermediates in organic synthesis. They also have found many of applications, that is, in agriculture and medicine. They are in use as pesticides, as well as in the rubber industries as vulcanization accelerators; and as antioxidants. Because they exhibit strong metal-binding capacity, they can act as in inhibitors of enzymes and have a profound effect on biological systems. Moreover, they have found application in the treatment of cancer and HIV.     

Molecular structure,molecular docking,thermal, spectroscopic and biological activity studies of bis‐Schiff base ligand and its metal complexes

Coordination compounds of Fe(III), Zn(II), Ni(II), Co(II), Cu(II), Cd(II) and Mn(II) ions were synthesized from the ligand [4,4′‐((((ethane‐1,2‐diylbis(oxy))bis(2,1‐phenylene))bis(methanylylidene))bis(azanylylidene))diphenol]ethane (H₂L) derived from the condensation of bisaldehyde and 4‐aminophenol. Microanalysis, magnetic susceptibility, infrared, ¹H NMR and mass spectroscopies, molar conductance, X ray powder diffraction and thermal analysis were used to confirm the structure of the synthesized chelates. According to the data obtained, the composition of the 1:1 metal ion–bis‐Schiff base ligand was found to be [M(H₂L)(H₂O)₂]Cl_n (M = Zn(II), Ni(II), Co(II), Cu(II), Cd(II) and Mn(II), n = 2; Fe(III), n = 3). Magnetic susceptibility measurements and reflectance spectra suggested an octahedral geometry for the complexes. Central metals ions and bis‐Schiff base coordinated together via O2 and N2 donor sites which as evident from infrared spectra. The Gaussian09 program was applied to optimize the structural formula for the investigated Schiff base ligand. The energy gaps and other important theoretical parameters were calculated applying the DFT/B3LYP method. Molecular docking using AutoDock tools was utilized to explain the experimental behaviour of the Schiff base ligand towards proteins of Bacillus subtilis (5 h67), Escherichia coli (3 t88), Proteus vulgaris (5i39) and Staphylococcus aureus (3ty7) microorganisms through theoretical calculations. The docked protein receptors were investigated and the energies of hydrogen bonding were calculated. These complexes were then subjected to in vitro antibacterial studies against several organisms, both Gram negative (P. vulgaris and E. coli) and Gram positive (S. pyogones and B. subtilis). The ligand and metal complexes exhibited good microbial activity against the Gram‐positive and Gram‐negative bacteria.     

Transient and steady state creep of Al-4.5 wt.% Mg during phase transformation

Transient and steady state creep of Al-4.5 wt. % Mg alloy was studied under various constant stresses ranging from 91 MPa to 117 MPa in the temperature range from 473 K to 553 K. The results of creep characteristics have shown two main deformation temperature regions (below 493 K and above 513 K as well as a transient region between these temperatures). Peak values of transient creep parametersB andn were obtained at 493 K. The transient creep parameterB was related to the steady state creep rate _st through the exponent which was found to range from 0.85 to 0.5. The stress exponentm of the steady state creep has been found to be minimum at the steady state strain peaks, which is characteristic of dislocation climb along the grain boundaries. Microstructural analysis confirmed that the above mentioned mechanism took place in the dissolution region of-phase.