On m-Ary Overpartitions

Presently there are a lot of activities in the study of overpartitions, objects that were discussed by MacMahon, and which have recently proven useful in several combinatorial studies of basic hypergeometric series. In this paper we study some similar objects, which we name m-ary overpartitions. We consider divisibility properties of the number of m-ary overpartitions of a natural number, and we prove a theorem which is a lifting to general m of the well-known Churchhouse congruences for the binary partition function. Received October 11, 2004     

Infinitely many congruences modulo 5 for 4-colored Frobenius partitions

In his 1984 AMS Memoir, Andrews introduced the family of functions \(c\phi _k(n),\) which denotes the number of generalized Frobenius partitions of \(n\) into \(k\) colors. Recently, Baruah and Sarmah, Lin, Sellers, and Xia established several Ramanujan-like congruences for \(c\phi _4(n)\) relative to different moduli. In this paper, employing classical results in \(q\)-series, the well-known theta functions of Ramanujan, and elementary generating function manipulations, we prove a characterization of \(c\phi _4(10n+1)\) modulo 5 which leads to an infinite set of Ramanujan-like congruences modulo 5 satisfied by \(c\phi _4.\) This work greatly extends the recent work of Xia on \(c\phi _4\) modulo 5.     

Progress towards the synthesis of Urukthapelstatin A and two analogues

We report our progress toward the synthesis of Urukthapelstatin A (Ustat A) and two analogues. Our retrosynthetic strategy involved the synthesis of three fragments: a tri-heteroaromatic moiety, a phenyl oxazole fragment, and a dipeptide. Described are the syntheses of three unique tri-heteroaromatic moieties. In addition, the corresponding linear precursors of Ustat A and two analogues are presented.     

Anisotropic effective core potentials

We present a convenient method for accounting for the anisotropy of partially filled d shells that are incorporated in effective core potentials by including the leading anisotropy term of the d-type electron density, which is the quadrupole moment, as an electrostatic potential energy operator in the model Hamiltonian. We present sample calculations on the cobalt hydride and dicobalt systems. We find the quadrupole anisotropy to have a very large effect in the distance regime of CoH. In the dicobalt system, which has a relatively long internuclear distance, the quadrupole anisotropy shifts the equilibrium bond length by nearly 0.02 bohr.     

Quick assessment methodology for reliability of solder joints in ball grid array (BGA) assembly—Part II: Reliability experiment and numerical simulation

In the present study, a facility, i.e., a mechanical deflection system (MDS), was established and applied to assess the long-term reliability of the solder joints in plastic ball grid array (BGA) assembly. It was found that the MDS not only quickly assesses the long-term reliability of solder joints within days, but can also mimic similar failure mechanisms in accelerated thermal cycling (ATC) tests. Based on the MDS and ATC reliability experiments, the acceleration factors (AF) were obtained for different reliability testing conditions. Furthermore, by using the creep constitutive relation and fatigue life model developed in part I, a numerical approach was established for the purpose of virtual life prediction of solder joints. The simulation results were found to be in good agreement with the test results from the MDS. As a result, a new reliability assessment methodology was established as an alternative to ATC for the evaluation of long-term reliability of plastic BGA assembly. The project supported by the National Natural Science Foundation of China (59705008)     

Comment and evaluation concerning some partial wave electron scattering factors frequently used in gas electron diffraction

An evaluation is presented of some recently published partial wave electron scattering factors for neutral atoms which are frequently used in structural studies by gas electron diffraction. Significant corrections are given for 3 of the 75 elements which were treated.     

Orientational order and finite strain in nematic elastomers

Nematic elastomers exhibit large, spontaneous shape changes at the transition from the high-temperature isotropic phase to the low-temperature nematic phase. These finite deformations are studied here in the context of a nonlinear, properly invariant, variational theory that couples the orientational order and elastic deformation. The theory is based on the minimization of a free-energy functional that consists of two contributions: a nematic one due to the interaction of the mesogenic units and an elastic one arising from the stretching of the cross-linked polymer chains. Suitable choices for these two contributions allow for large, reversible, spontaneous shape changes in which the elastic deformation can affect the isotropic-nematic transition temperature. The change in transition temperature as well as the magnitude of the resulting spontaneous deformation is illustrated for various parameter values. The theory includes soft elasticity as a special case but is not restricted to it.     

ROLE OF THE TRYPTOPHAN FLUORESCENT STATE IN THE ULTRAVIOLET-INDUCED INACTIVATION OF β-TRYPSIN*

Abstract— Stern-Volmer quenching constants for β-trypsin at pH 3 were determined for fluorescence quenching by histidine, acrylamide, and nitrate ion. A modified Stern-Volmer plot (Lehrer, 1971) was employed to show that all of the fluorescent tryptophanyl residues of β-trypsin were equally susceptible to quenching by acrylamide at pH 3 when the enzyme was either in its native conformation or denatured in 6 M guanidine hydrochloride (GuHCl). Fluorescence lifetime measurements indicated that acrylamide quenched β-trypsin fluorescence by a purely collisional mechanism. Solvation of tryptophanyl residues of the protein was maximal at 2.5 M GuHCl, as monitored by fluorescence emission wavelength.
Investigations of the ultraviolet-induced inactivation of β-trypsin at 295 nm were performed in the presence of acrylamide at pH 3. The quantum yields for enzyme inactivation and indole destruction (determined using the PDAB reagent) were unchanged upon depopulation of the fluorescent state by 65 per cent, whether the enzyme was in its native conformation or denatured by 6 M GuHCl. It is concluded that the fluorescent state of tryptophanyl residues of β-trypsin is not involved in enzyme inactivation or tryptophan destruction.     

Congruences for the coefficients of the Gordon and McIntosh mock theta function $$\xi (q)$$ ξ ( q )

The Ramanujan Journal - Recently Gordon and McIntosh introduced the third order mock theta function $$\xi (q)$$ defined by $$\begin{aligned} \xi (q)=1+2\sum _{n=1}^{\infty...