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.     

Kibdelones: novel anticancer polyketides from a rare Australian actinomycete

The kibdelones are a novel family of bioactive heterocyclic polyketides produced by a rare soil actinomycete, Kibdelosporangium sp. (MST-108465). Complete relative stereostructures were assigned to kibdelones A-C (1-3), kibdelone B rhamnoside (5), 13-oxokibdelone A (7), and 25-methoxy-24-oxokibdelone C (8) on the basis of detailed spectroscopic analysis and chemical interconversion, as well as mechanistic and biosynthetic considerations. Under mild conditions, kibdelones B (2) and C (3) undergo a facile equilibration to kibdelones A-C (1-3), while kibdelone B rhamnoside (5) equilibrates to a mixture of kibdelone A-C rhamnosides (4-6). A plausible mechanism for this equilibration is proposed and involves air oxidation, quinone/hydroquinone redox transformations, and a choreographed sequence of keto/enol tautomerizations that aromatize ring C via a quinone methide intermediate. Kibdelones exhibit potent and selective cytotoxicity against a panel of human tumor cell lines and display significant antibacterial and nematocidal activity.     

Rapid aerobic iodination of arenes mediated by hypervalent iodine in fluorinated solvents

Arenes are rapidly converted to the corresponding iodides by aerobic oxidative iodination at room temperature by treatment with iodine and catalytic quantities of nitrous acid in a fluorinated solvent. Dichloroiodic acid is proposed as the actual iodination reagent.     

Is the Home Equity Conversion Mortgage in the United States sustainable? Evidence from pricing mortgage insurance premiums and non-recourse provisions using the conditional Esscher transform

The purpose of this paper is to build a modeling and pricing framework to investigate the sustainability of the Home Equity Conversion Mortgage (HECM) program in the United States under realistic economic scenarios, i.e., whether the premium payments cover the fair premiums for the inherent risks in the HECM program. We note that earlier HECM models use static mortality tables, neglecting the dynamics of mortality rates and extreme mortality jumps. The earlier models also assume housing prices follow a geometric Brownian motion, which contradicts the fact that housing prices exhibit strong autocorrelation and varying volatility over time. To solve these problems, we propose a generalized Lee-Carter model with asymmetric jump effects to fit the mortality data, and model the house price index via an ARIMA-GARCH process. We then employ the conditional Esscher transform to price the non-recourse provision of reverse mortgages and compare it with the calculated mortgage insurance premiums. The HECM program turns out to be sustainable based on our model setup and parameter settings.     

Line graphs: Their maximum nullities and zero forcing numbers

The maximum nullity over a collection of matrices associated with a graph has been attracting the attention of numerous researchers for at least three decades. Along these lines various zero forcing parameters have been devised and utilized for bounding the maximum nullity. The maximum nullity and zero forcing number, and their positive counterparts, for general families of line graphs associated with graphs possessing a variety of specific properties are analysed. Building upon earlier work, where connections to the minimum rank of line graphs were established, we verify analogous equations in the positive semidefinite cases and coincidences with the corresponding zero forcing numbers. Working beyond the case of trees, we study the zero forcing number of line graphs associated with certain families of unicyclic graphs.     

Comparison of δ81Br and δ37Cl composition of volatiles,salt precipitates,and associated water in terrestrial evaporative saline lake systems

This study provides the first characterization of the variability of bromine and chlorine stable isotopic composition in evaporites, associated residual brines, and shoreline gases in terrestrial evaporative saline lakes. The lakes investigated here are groundwater discharge locations, and include both potash-rich alkaline lakes and sodic-dominated neutral pH lakes at a variety of salinities and evaporative stages. The chlorine and bromine isotope systems behave consistently different during evaporative salt precipitation, with ³⁷Cl more enriched in the salt than in the fluid, but ⁸¹Br more enriched in the fluid compared with the precipitated salt. The ⁸¹Br concentration of shore off-gassing was even smaller than mineral precipitate compositions. The trends observed for bromine isotopes are surprising compared with published laboratory studies, indicating that a process besides inorganic mineral precipitation is affecting δ⁸¹Br. Additional processes explored include diffusion, salt deflation, microbial and photolytic conversion to the gas phase, and oxidative bromination of organic matter.

Dedicated to Professor Peter Fritz on the occasion of his 80th birthday     

TLC Image Capture and Analysis by use of a Prototype Device for Visualizing Fluorescence

JPC – Journal of Planar Chromatography – Modern TLC - This paper reports the evaluation of a novel, low-cost imaging device for use in TLC — a commercial flat-bed scanner modified...     

Synthesis and photophysical behavior of a novel zinc phthalocyanine containing a single carboxylic acid and three phenylthio substituents

Zinc 2, (3)-tri-(phenylthio)-2, (3)-carboxy phthalocyanine (ZnPc(COOH)(SPh)₃), zinc 2, (3)-tetra-(phenylthio) phthalocyanine (ZnPc(SPh)₄) and 2, (3)-tetra-(phenylthio) phthalocyanine (H₂Pc(SPh)₄) were synthesized and their photophysical behavior were compared with those of a number of zinc phthalocyanine (ZnPc) derivatives. ZnPc(COOH)(SPh)₃ and ZnPc(SPh)₄ had similar fluorescence (Φ_F=0.14) and triplet state (Φ_T=0.65) quantum yields in dimethylsulfoxide, hence showing no effects of the replacement of one of the phenylthio groups with a carboxylic acid group. ZnPc(COOH)(SPh)₃ displayed a slightly shorter triplet lifetime (τ_T=331 μs) than ZnPc (τ_T=350 μs) in DMSO, but within the range of ZnPc derivatives. The triplet lifetime for ZnPc(COOH)(SPh)₃ is much longer than for the symmetrical derivative (ZnPc(SPh)₄) with τ_T=149 μs in DMSO.     

Peptide asparaginyl ligases——renegade peptide bond makers

Making peptide bonds is tightly controlled by genetic code and machinery which includes cofactors,ATP,and RNAs.In this regard,the stand-alone and genetic-code-independent peptide ligases constitute a new family of renegade peptide-bond makers.A prime example is butelase-1,an Asn/Asp(Asx)-specific ligase that structurally belongs to the asparaginyl endopeptidase family.Butelase-1 specifically recognizes a C-terminal Asx-containing tripeptide motif,Asn/Asp-Xaa-Yaa(Xaa and Yaa are any amino acids),to form a site-specific Asn-Xaa peptide bond either intramolecularly as cyclic proteins or intermolecularly as modified proteins.Our work in the past five years has validated that butelase-1 is a potent and versatile ligase.Here we review the advances in ligases,with a focus on butelase-1,and their applications in engineering bioactive peptides and precision protein modifications,antibody-drug conjugates,and live-cell labeling.