Change of Base in Bailey Pairs

Versions of Bailey's lemma which change the base from q to q ² or q ³ are given. Iterates of these versions give many new versions of multisum Rogers-Ramanujan identities.     

Stochastic nonlinear dynamics of interpersonal and romantic relationships

Current theories from biosocial (e.g., the role of neurotransmitters in behavioral features), ecological (e.g., cultural, political, and institutional conditions), and interpersonal (e.g., attachment) perspectives have grounded interpersonal and romantic relationships in normative social experiences. However, these theories have not been developed to the point of providing a solid theoretical understanding of the dynamics present in interpersonal and romantic relationships, and integrative theories are still lacking. In this paper, mathematical models are used to investigate the dynamics of interpersonal and romantic relationships, via ordinary and stochastic differential equations, in order to provide insight into the behaviors of love. The analysis starts with a deterministic model and progresses to nonlinear stochastic models capturing the stochastic rates and factors (e.g., ecological factors, such as historical, cultural and community conditions) that affect proximal experiences and shape the patterns of relationship. Numerical examples are given to illustrate various dynamics of interpersonal and romantic behaviors with particular emphases placed on sustained oscillations and transitions between locally stable equilibria that are observable in stochastic models (closely related to real interpersonal dynamics), but absent in deterministic models.     

U + U potential in the sudden and adiabatic approximation

A recent approach for calculating both the real and imaginary parts of the ion-ion potential has been modified to produce the ground state properties of separate nuclei. This approach is used to study both the energy and orientation dependence of the optical potential between two U nuclei adopting the sudden and adiabatic approximations.     

Characterization of fe bearing compounds in environmental samples

Using⁵⁷Mössbauer spectroscopy and neutron activation analysis, various kinds of environmental samples have been studied, in order to demonstrate that the combination of a phase sensitive and a multi-element technique is a powerful tool for studying environmental problems.     

Spectral Studies and Cathodic Reduction of some Thiazolylazo Derivatives

The structure of the 2-thiazolylazosalicylic acid molecule, TAS, has been determined by means of quantum SCF-CI calculations. The ionization potential and the electron affinity of TAS molecule were calculated to have the values 9.057 and 2.56 eV respectively. The solvation energies in different solvents, and the bond orders of the TAS molecule were calculated for the neutral state, the oxidized form (the cation) and the reduced form (the anion). Mixed solvent studies were carried out with TAS and 2-benzothiazolylazosalicylic acid (BTAS), using polar solvents (EtOH and MeOH) to confirm the formation of a solvent-solute complex. The azo group in the TAS molecule nas a considerable contribution in the SCFLUMO; thus cathodic reduction has been focused on the azo group and was verified experimentally by cathodic reduction.     

Influence of maleic anhydride grafted ethylene propylene diene monomer (MAH-g-EPDM) on the properties of EPDM nanocomposites reinforced by halloysite nanotubes

Ethylene propylene diene monomer grafted with maleic ahydride (MAH-g-EPDM) was prepared by peroxide-initiated melt grafting of MAH onto EPDM using a HAAKE internal mixer at 180 °C and 60 rpm for 5 min. The effect of MAH-g-EPDM compatibilizer on the interactions, and tensile and morphological properties of halloysite nanotubes (HNTs) filled EPDM nanocomposites was investigated. The tensile properties of the nanocomposites were influenced by two major factors. The hydrogen bonding between MAH-g-EPDM and HNTs, which was confirmed by attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR), as well as the formation of EPDM-rich and HNT-rich areas, are the dominant effects on the tensile strength of the nanocomposites at low and high HNT loading, respectively. It was found that the cure time (t₉₀), maximum torque (M_H) and minimum torque (M_L) of the compatibilized nanocomposites were increased after adding MAH-g-EPDM. The reinforcement mechanism of the compatibilized and un-compatibilized EPDM/HNT nanocomposites was also investigated based on morphological observations of the nanocomposites.     

Enol ethers as substrates for efficient Z- and enantioselective ring-opening/cross-metathesis reactions promoted by stereogenic-at-Mo complexes: utility in chemical synthesis and mechanistic attributes

The first examples of catalytic enantioselective ring-opening/cross-metathesis (EROCM) reactions that involve enol ethers are reported. Specifically, we demonstrate that catalytic EROCM of several oxa- and azabicycles, cyclobutenes and a cyclopropene with an alkyl- or aryl-substituted enol ether proceed readily in the presence of a stereogenic-at-Mo monopyrrolide-monoaryloxide. In some instances, as little as 0.15 mol % of the catalytically active alkylidene is sufficient to promote complete conversion within 10 min. The desired products are formed in up to 90% yield and >99:1 enantiomeric ratio (er) with the disubstituted enol ether generated in >90% Z selectivity. The enol ether of the enantiomerically enriched products can be easily differentiated from the terminal alkene through a number of functionalization procedures that lead to the formation of useful intermediates for chemical synthesis (e.g., efficient acid hydrolysis to afford the enantiomerically enriched carboxaldehyde). In certain cases, enantioselectivity is strongly dependent on enol ether concentration: larger equivalents of the cross partner leads to the formation of products of high enantiomeric purity (versus near racemic products with one equivalent). The length of reaction time can be critical to product enantiomeric purity; high enantioselectivity in reactions that proceed to >98% conversion in as brief a reaction time as 30 s can be nearly entirely eroded within 30 min. Mechanistic rationale that accounts for the above characteristics of the catalytic process is provided.     

Antitumor Activity of Some Novel 1,2,5-Thiadiazole Derivatives

Some novel thiourea,1,2,4-triazole, quinazoline, thieno[2,3-d]pyrimi-dine, and thiazolidine derivatives were synthesized to evaluate their antitumor activity. Compound (3f) is nearly as active as reference drug, (Doxorubicin) as positive control.