The representation of integers by binary additive forms

Let a, b and n be integers with 3. We show that, in the sense of natural density, almost all integers represented by the binary form axⁿ – byⁿ are thus represented essentially uniquely. By exploiting this conclusion, we derive an asymptotic formula for the total number of integers represented by such a form. These conclusions augment earlier work of Hooley concerning binary cubic and quartic forms, and generalise or sharpen work of Hooley, Greaves, and Skinner and Wooley concerning sums and differences of two nth powers.     

Review on screening and analysis techniques for hemoglobin variants and thalassemia

Thalassemia involves gene mutation that causes the production of an insufficient amount of normal structure globin chains while Hb variant involves gene mutation that causes the change in type or number of amino acid of the globin chain. It has been reported that some 200 million people worldwide had hemoglobinopathies of some sort. Attempts to develop effective and economical techniques for screening and analysis of thalassemia and Hb variants have become very important. In this review, we report the different techniques available, ranging from initial screening to extensive analysis, comparing advantages and disadvantages. Some indirect studies related to thalassemia indication and treatment follow-up are also included. We hope that information on these various techniques would be useful for some scientists who are working on development of a new technique or improving the existing ones.     

Preparation and crystal structure of ternary rare-earth platinum metal aluminides R2T3Al9 (T=Rh, Ir, Pd) with Y2Co3Ga9-type structure and magnetic properties of the iridium compounds

The ternary aluminides R₂Rh₃Al₉ (R=Y, La-Nd, Sm, Gd-Tm, Lu), R₂Ir₃Al₉ (R=Y, La-Nd, Sm, Gd-Lu), and R₂Pd₃Al₉ (R=Y, Gd-Tm) have been prepared by arc melting of the elemental components with an excess of aluminum and dissolving the aluminum-rich matrix in hydrochloric acid. They crystallize with Y₂Co₃Ga₉-type structure: Cmcm, Z=4. The crystal structures of Ho₂Rh₃Al₉ and Er₂Ir₃Al₉ have been refined from single-crystal X-ray data; Ho₂Rh₃Al₉: a=1316.8(3) pm, b=760.2(2) pm, c=933.7(2) pm, R=0.044 for 255 structure factors and 27 variables; Er₂Ir₃Al₉: a=1313.8(2) pm, b=758.5(1) pm, c=933.8(2) pm, R=0.057 (392 F values, 27 variables). The structure may be viewed as consisting of atomic layers of the compositions A=R₂Al₃ and B=T₃Al₆ which alternate in the sequence ABAB along the z direction. Approximately 33% and 27% of the A layers were found to be misplaced in the crystals investigated for Ho₂Rh₃Al₉ and Er₂Ir₃Al₉, respectively. The magnetic properties of most iridium-containing compounds have been determined with a superconducting quantum interference device magnetometer. The yttrium and the lanthanum compounds show Pauli paramagnetism, others reflect the magnetic behavior of the rare-earth components. The magnetic ordering temperatures are all lower than 20 K.     

ON A PROBLEM OF SUMS OF MIXED POWERS （II）

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A survey of variants and extensions of the location-routing problem

This is a review of the literature on variants and extensions of the standard location-routing problem published since the last survey, by Nagy and Salhi, appeared in 2006. We propose a classification of problem variants, provide concise paper excerpts that convey the central ideas of each work, discuss recent developments in the field, and list promising topics for further research.     

Indirect resolution of baclofen enantiomers from pharmaceutical dosage form by reversed-phase liquid chromatography after derivatization with Marfey's reagent and its structural variants

A high-performance liquid chromatographic (HPLC) method was developed for chiral assay of baclofen enantiomers in pharmaceutical formulations using an indirect approach. Baclofen enantiomers were derivatized with Marfey's reagent (FDNP-L-Ala-NH2) and its structural variants FDNP-L-Phe-NH2, FDNP-L-Val-NH2, FDNP-L-Leu-NH2 and FDNP-L-Pro-NH2. The resultant diastereomers were separated on RP-TLC [triethylammonium phosphate buffer (pH 4.0, 50 mm)-acetonitrile, 50:50] and on a C18 column using a linear gradient (45 min) of acetonitrile and 0.01% aqueous trifluoroacetic acid (TFA) with UV detection at 340 nm. The differences in the retention times (Delta t R) of diastereomers due to the five chiral reagents were compared. The maximum and minimum difference in retention times between separated diastereomers was for FDNP-L-Leu-NH2 and FDNP-L-Pro-NH2, respectively. The effect of flow rate, acetonitrile content and TFA concentration on resolution was studied. The method was validated for linearity, repeatability, limit of detection and limit of quantification.     

Copy number variants calling for single cell sequencing data by multi-constrained optimization

Variations in DNA copy number carry important information on genome evolution and regulation of DNA replication in cancer cells. The rapid development of single-cell sequencing technology allows one to explore gene expression heterogeneity among single-cells, thus providing important cancer cell evolution information. Single-cell DNA/RNA sequencing data usually have low genome coverage, which requires an extra step of amplification to accumulate enough samples. However, such amplification will introduce large bias and makes bioinformatics analysis challenging. Accurately modeling the distribution of sequencing data and effectively suppressing the bias influence is the key to success variations analysis.Recent advances demonstrate the technical noises by amplification are more likely to follow negative binomial distribution, a special case of Poisson distribution. Thus, we tackle the problem CNV detection by formulating it into a quadratic optimization problem involving two constraints, in which the underling signals are corrupted by Poisson distributed noises. By imposing the constraints of sparsity and smoothness, the reconstructed read depth signals from single-cell sequencing data are anticipated to fit the CNVs patterns more accurately. An efficient numerical solution based on the classical alternating direction minimization method (ADMM) is tailored to solve the proposed model. We demonstrate the advantages of the proposed method using both synthetic and empirical single-cell sequencing data. Our experimental results demonstrate that the proposed method achieves excellent performance and high promise of success with single-cell sequencing data.     

The Role of Single-Nucleotide Variants of NOS1, NOS2, and NOS3 Genes in the Comorbidity of Arterial Hypertension and Tension-Type Headache

Patients with tension-type headache (TTH) have an increased risk of developing arterial hypertension (AH), while hypertensive subjects do seem to have an increased risk of TTH. We searched for full-text English publications in databases using keywords and combined word searches over the past 15 years. In addition, earlier publications of historical interest were included in the review. In our review, we summed up the single nucleotide variants (SNVs) of Nitric Oxide Synthases (NOSs) genes involved in the development of essential AH and TTH. The results of studies we discussed in this review are contradictory. This might be due to different designs of the studies, small sample sizes in some of them, as well as different social and geographical characteristics. However, the contribution of genetic and environmental factors remains understudied. This makes the issue interesting for researchers, as understanding these mechanisms can contribute to a search for new approaches to pathogenetic and disease-modifying treatment of the AH and TTH phenotype. New drugs against AH and TTH can be based on inhibition of nitric oxide (NO) production, blockade of steps in the NO-cGMP pathway, or NO scavenging. Indeed, selective neuronal NOS (n-NOS) and inducible NOS (i-NOS) inhibitors are already in early clinical development.     

Adsorption of deamidated antibody variants on macroporous and dextran-grafted cation exchangers: II. Adsorption kinetics

Single and multicomponent batch adsorption kinetics were obtained for deamidated mAb variants on two commercial cation exchangers, one with an open macroporous structure--UNOsphere S--and the other with charged dextran grafts--Capto S. The adsorption kinetics for the macroporous matrix was found to be controlled largely by pore diffusion. The effective diffusivity estimated from single component data was a fraction of the mAb free solution diffusivity, and its value could be used to accurately predict the adsorption kinetics for two- and three-component systems. In this case, when two or more variants were adsorbed simultaneously, both experimental and predicted results showed a temporary overshoot of the amount adsorbed above the equilibrium value for the more deamidated variant followed by a gradual approach to equilibrium. Adsorption rates on the dextran grafted material were much faster than those observed for the macroporous matrix for both single component and simultaneous adsorption cases. In this case, no significant overshoot was observed for the more deamidated forms. The Capto S adsorption kinetics could be described well by a diffusion model with an adsorbed phase driving force for single component adsorption and for the simultaneous adsorption of multiple variants. However, this model failed to predict the adsorption kinetics when more deamidated forms pre-adsorbed on the resin were displaced by less deamidated ones. In this case, the kinetics of the displacement process was much slower indicating that the pre-adsorbed components severely hindered transport of the more strongly bound variants. Overall, the results indicate that despite the lower capacity, the macroporous resin may be more efficient in process applications where displacement of one variant by another takes place as a result of the faster and more predictable kinetics.