We determine the characteristic polynomials of the matrices $[q^{\,j-k}+t]_{1\le \,j,k\le n}$ and $[q^{\,j+k}+t]_{1\le \,j,k\le n}$ for any complex number $q\not =0,1$. As an application, for complex numbers $a,b,c$ with $b\not =0$ and $a^2\not =4b$, and the sequence $(w_m)_{m\in \mathbb Z}$ with $w_{m+1}=aw_m-bw_{m-1}$ for all $m\in \mathbb Z$, we determine the exact value of $\det [w_{\,j-k}+c\delta _{jk}]_{1\le \,j,k\le n}$.

It is generally accepted that high-oleic crops have at least 70% oleate. As compared to their normal-oleic counterparts, oil and food products made from high-oleic peanut have better keeping quality and are much healthier. Therefore, high-oleic peanut is well recognized by processors and consumers. However, owing to the limited availability of high-oleic donors, most present-day high-oleic peanut varietal releases merely have F435 type FAD2 mutations. Through screening of a mutagenized peanut population of 15L46, a high-yielding peanut line with desirable elliptical oblong large seeds, using near infrared model for predicting oleate content in individual single seeds, high-oleic peanut mutants were identified. Sequencing FAD2A and FAD2B of the mutants along with the wild type revealed that these mutants possessed G448A FAD2A (F435 type FAD2A mutation) and G558A FAD2B (non-F435 type FAD2B mutation). Expression of the wild and mutated type FAD2B in yeast verified that the functional mutation contributed to the high-oleic phenotype in these mutants. The mutants provided additional high-oleic donors to peanut quality improvement.

Nutritional Risk Screening index is a standard tool to assess nutritional risk, but epidemiological data are scarce on controlling nutritional status (CONUT) as a prognostic marker in acute haemorrhagic stroke (AHS). We aimed to explore whether the CONUT may predict a 3-month functional outcome in AHS. In total, 349 Chinese patients with incident AHS were consecutively recruited, and their malnutrition risks were determined using a high CONUT score of ≥ 2. The cohort patients were divided into high-CONUT (≥ 2) and low-CONUT (< 2) groups, and primary outcomes were a poor functional prognosis defined as the modified Rankin Scale (mRS) score of ≥ 3 at post-discharge for 3 months. Odds ratios (OR) with 95 % confidence intervals (CI) for the poor functional prognosis at post-discharge were estimated by using a logistic analysis with additional adjustments for unbalanced variables between the high-CONUT and low-CONUT groups. A total of 328 patients (60·38 ± 12·83 years; 66·77 % male) completed the mRS assessment at post-discharge for 3 months, with 172 patients at malnutrition risk at admission and 104 patients with a poor prognosis. The levels of total cholesterol and total lymphocyte counts were significantly lower in high-CONUT patients than low-CONUT patients (P = 0·012 and < 0·001, respectively). At 3-month post discharge, there was a greater risk for the poor outcome in the high-CONUT compared with the low-CONUT patients at admission (OR: 2·32, 95 % CI: 1·28, 4·17). High-CONUT scores independently predict a 3-month poor prognosis in AHS, which helps to identify those who need additional nutritional managements.

Biological materials represent a major source of inspiration to engineer protein-based polymers that can replicate the properties of living systems. Combined with our ability to control the molecular structure of proteins at the single amino acid level, this results in a vast array of attractive possibilities for materials science, an interest that is undeniably related to simplified procedures in gene synthesis, cloning, and biotechnological production. In parallel, it has been increasingly appreciated that living organisms exploit liquid–liquid phase separation (LLPS) to fabricate extracellular structures. In this article, we discuss the central role of protein LLPS in the fabrication of selected biological structures, including biological adhesives and hard biomolecular composites, and how physicochemical lessons from these systems are being replicated in synthetic analogs. Recent translational applications of protein LLPS are highlighted, notably aqueous-resistant adhesives, stimuli-responsive therapeutics carriers, and matrix materials for green structural composites.

CrFeNiTix (x = 0.2, 0.3, 0.4, 0.5, and 0.6 molar ratio) compositionally complex alloys were fabricated by vacuum arc melting to investigate the microstructure, hardness, and compressive properties. The results revealed that CrFeNiTix alloys consisted of the principal face-centered cubic (FCC) phase and body-centered cubic (BCC) solid solution, with an amount of (Ni, Ti)-rich hexagonal close-packed phase. CrFeNiTix alloys exhibited the typical dendrite. Ti0.2 and Ti0.3 alloys were composed of FCC and BCC solid solutions in the dendrite, as well as ε (Ni3Ti) and R (Ni2.67Ti1.33) phases in the inter-dendrite, simultaneously. For Ti0.4, Ti0.5, and Ti0.6 alloys, (Fe, Cr)-rich solid solution separated out and ε phase transformed into R phase gradually. Meanwhile, TEM analysis indicated that Ti0.4 alloy matrix consisted of the principal FCC phase containing (Ni, Ti)-rich intragranular nanoprecipitates. The hardness values of CrFeNiTix alloys were increased with the addition of Ti content and the high compressive strength of CrFeNiTix alloys was maintained, which was attributed to the solid solution strengthening and precipitation hardening.

Previous studies show inconsistent associations between α-linolenic acid (ALA) and risk of CHD. We aimed to examine an aggregate association between ALA intake and risk of CHD, and assess for any dose–response relationship. We searched the PubMed, EMBASE and Web of Science databases for prospective cohort studies examining associations between ALA intake and CHD, including composite CHD and fatal CHD. Data were pooled using random-effects meta-analysis models, comparing the highest category of ALA intake with the lowest across studies. Subgroup analysis was conducted based on study design, geographic region, age and sex. For dose–response analyses, we used two-stage random-effects dose–response models. In all, fourteen studies of thirteen cohorts were identified and included in the meta-analysis. The pooled results showed that higher ALA intake was associated with modest reduced risk of composite CHD (risk ratios (RR)=0·91; 95 % CI 0·85, 0·97) and fatal CHD (RR=0·85; 95 % CI 0·75, 0·96). The analysis showed a J-shaped relationship between ALA intake and relative risk of composite CHD (χ2=21·95, P<0·001). Compared with people without ALA intake, only people with ALA intake <1·4 g/d showed reduced risk of composite CHD. ALA intake was linearly associated with fatal CHD – every 1 g/d increase in ALA intake was associated with a 12 % decrease in fatal CHD risk (95 % CI −0·21, −0·04). Though a higher dietary ALA intake was associated with reduced risk of composite and fatal CHD, the excess composite CHD risk at higher ALA intakes warrants further investigation, especially through randomised controlled trials.

The exaggerated grain growth, anisotropic crystallite morphology, and thermal expansion are the main reasons for the microcracking of sintered TiB2, wherein grain coarsening and anisotropic crystallite morphology are believed to be controlled by the surface stabilities of TiB2. To deeply understand the grain growth mechanism, the anisotropic stability and bonding features of TiB2 surfaces, including $\left( {11\bar 20} \right)$ , two types of (0001), and three types of $\left( {10\bar 10} \right)$ , are investigated by first-principles calculations. By employing the two-region modeling method, surface energies are calculated and the $\left( {11\bar 20} \right)$ surface is found to be more stable than (0001) and $\left( {10\bar 10} \right)$ surfaces. Hexagonal plate-like grain morphology is predicted. The different bonding conditions of surface Ti and B atoms contribute to the difference of surface structure relaxation between surfaces with Ti- and B-termination, which lead the B-terminated ones to be more stable. It is also found that the surface energies of TiB2 are much higher than those of ZrB2 with a similar structure, which may be responsible for the easy coarsening of TiB2.

Al1.3CrFeNi eutectic high entropy alloy was designed and prepared by arc-melting to investigate the microstructure and oxidation behaviors at 1000 °C. The XRD pattern shows that this alloy had a double bcc/B2 structure. SEM images indicates that the microstructure of the alloy is composed of two precipitates of [Cr, Fe] solid solution and NiAl intermetallic, which form the typical eutectic structure. To explore the thermal application of Al1.3CrFeNi alloy, the oxidation behavior of Al1.3CrFeNi alloy at 1000 °C was investigated. From XRD and SEM results, it could be concluded that Al2O3 and Cr2O3 were the predominant oxides during the oxidation process. In addition, spinel like FeCr2O4 was also observed in the oxide scale. According to the analysis of oxide precipitates, the whole process of oxides’ formation was discussed and a simplified oxidation dynamic model of Al1.3CrFeNi alloy at 1000 °C was obtained. This could promote the development of thermal applications in multi-component alloys field.

We investigated the boron isotopic composition in loess–paleosol sequences in five different profiles in the Chinese Loess Plateau. Three possible boron sources are identified: atmospheric input, carbonates, and weathered silicate rocks. Variations of [Sr], [B], δ11B and the magnetic susceptibility correlate well with the pedogenetic intensity in three out of the five studied profiles, where pedogenesis under a cold–dry climate indicates lower δ11B, lower [B], lower magnetic susceptibility and higher [Sr] values. Exceptions to the variations between the δ11B and other known proxies were observed in arenaceous soils and the Red Clay sequence: the former suggested that vertical redistribution probably occurred with the boron migration, and the latter indicated an unknown mechanism of susceptibility enhancement. A better correlation between the δ11B and magnetic susceptibility and the quantitative estimation of boron budget from each source confirms the influence of paleoenvironmental changes on boron geochemical cycle. Significant positive correlations in Sr/Ca vs. B/Ca and Mg/Ca vs. B/Ca reflect consistent enrichment behavior of those mobile elements into calcium carbonate. The preliminary results imply that boron isotopic compositions in soils can be a potential geochemical proxy to reconstruct the paleoenvironmental changes in loess–paleosol sequences.

The three-dimensional instabilities of axisymmetric flow are investigated in a laterally heated vertical cylinder by linear stability analysis. Heating is confined to a central zone on the sidewall of the cylinder, while other parts of the sidewall are insulated and both ends of the cylinder are cooled. The length of the heated zone equals the radius of the cylinder. For three different aspect ratios, $A= 1.92 $, 2, 2.1 ($A=\mathrm{height}$/radius), the dependence of the critical Rayleigh number on the Prandtl number (from 0.02 to 6.7) has been studied in detail. For such a kind of laterally heated convection, some interesting stability results are obtained. A monotonous instability curve is obtained for $A= 1.92 $, while the instability curves for $A= 2 $ and $A= 2.1 $ are non-monotonous and multivalued. In particular, an instability island has been found for $A=2$. Moreover, mechanisms corresponding to different instability results are obtained when the Prandtl number changes. At small Prandtl number, the flow is oscillatory unstable, which is dominated by hydrodynamic instability. At intermediate Prandtl number, the interaction between buoyancy and shear in the base flow plays a more important role than pure hydrodynamic instability. At even higher Prandtl number, Rayleigh–Bénard instability becomes the dominant process and the flow loses stability through steady bifurcation.

For $n= 1, 2, 3, \ldots $ let ${S}_{n} $ be the sum of the first $n$ primes. We mainly show that the sequence ${a}_{n} = \sqrt[n]{{S}_{n} / n}~(n= 1, 2, 3, \ldots )$ is strictly decreasing, and moreover the sequence ${a}_{n+ 1} / {a}_{n} ~(n= 10, 11, \ldots )$ is strictly increasing. We also formulate similar conjectures involving twin primes or partitions of integers.

In this paper, motivated by Catalan numbers and higher-order Catalan numbers, we study factors of products of at most two binomial coefficients.

In this paper we derive congruences expressing Bell numbers and derangement numbers in terms of each other modulo any prime.

Let 𝒜={as(mod ns)}ks=0 be a system of residue classes. With the help of cyclotomic fields we obtain a theorem which unifies several previously known results related to the covering multiplicity of 𝒜. In particular, we show that if every integer lies in more than m0=⌊∑ ks=11/ns⌋ members of 𝒜, then for any a=0,1,2,… there are at least subsets I of {1,…,k} with ∑ s∈I1/ns=a/n0. We also characterize when any integer lies in at most m members of 𝒜, where m is a fixed positive integer.

The construction of the sorghum (Sorghum bicolor L. Moench) molecular genetic linkage map started in the early 1990s. Molecular genetic maps with a high density of markers covering almost the entire sorghum genome have been completed and integration of a sorghum genetic and physical map is under way. The correlation between genetic linkage groups and relevant chromosomes was established and the locations of the important structures of chromosomes, such as centromeres, long and short arms, nucleolus organizer region (NOR), etc., have been identified on the linkage groups. Molecular cytogenetic mapping of each chromosome has been advanced substantially. With continuing progress in the field, sequencing of the full sorghum genome and study of sorghum functional genomics will be initiated soon.

In 1950 Erdös proved that if $x\equiv2\,036\,812\ (\mo5\,592\,405)$ and $x\equiv3\ (\mo62)$, then $x$ is not of the form $2^n+p$, where $n$ is a non-negative integer and $p$ is a prime. In this note we present a theorem on integers of the form $2^n+cp$, in particular we completely determine all those integers $c$ relatively prime to $5\,592\,405$ such that the residue class $2\,036\,812(\mo5\,592\,405)$ contains integers of the form $2^n+cp$.

AMS 2000 Mathematics subject classification: Primary 11P32. Secondary 11A07; 11B25; 11B75

The magnetic properties and the domain structure of anisotropic melt-spun SmCo6.5Zr0.5 alloys with C addition was investigated by means of x-ray diffraction (XRD), magnetic measurement, and magnetic force microscopy. The XRD analyses showed that the addition of a few percent of C led to a significant increase in the coercivity and simultaneously affected the characterization of crystalline texture of the ribbons. The easy magnetization c axis changed from parallel to the ribbon plane for SmCo6.5Zr0.5 ribbons to normal to the ribbon plane for SmCo6.5Zr0.5C0.25−0.75 ribbons. An optimal coercivity of 0.92 T was obtained for the SmCo6.5Zr0.5C0.5 ribbon spun at 5 m/s. The corresponding remanence measured normal or parallel to the ribbon plane was 7.1 kGs or 3.1 kGs, respectively. The domain structure was studied by magnetic force microscopey. A strip-shaped domain was observed on the surface of the SmCo6.5Zr0.5 ribbons and the walls lay straight and parallel. For C-doped ribbons, the domain walls formed a maze domain pattern of grains with c axis normal to the ribbon plane. Scanning electron micrographs showed that a dendrite structure was present in the SmCoZr ribbon surface, and C addition caused the above-mentioned dendrite to diminish.

The structure and magnetic properties of Nd8.4Fe86Mo1.1B4.5 nanostructured magnets prepared by mechanical alloying (MA), compared with those by mechanical milling (MM), were studied. The intrinsic coercivity μ0Hc, the reduced remanence Jr/Js, and the maximum magnetic energy product (BH)max for Nd8.4Fe86Mo1.1B4.5 magnets were prepared by MM were notably higher than the values of the corresponding MA-prepared samples. The average grain sizes of both α–Fe and Nd2Fe14B in the MM-prepared samples were measurably smaller than corresponding values of the MA-prepared samples. A more homogeneous distribution of α–Fe grains in the MM-prepared samples than in the MA-prepared samples was obtained.

A new method of epitaxial growth of CoSi2 film on Si substrate by ternary solid state interaction is investigated. XRD, RBS and TEM show that single-crystalline CoSi2 can be formed on both Si (111) and (100) substrates by using Co/Ti/Si or TiN/Co/Ti/Si multilayer. The evolution of multilayer structure and its resistivity is studied and epitaxy mechanism is discussed. Experimental results indicate strong affinity between Co and Si. During the ternary interaction the epitaxial CoSi2 can be grown directly on Si and its growth may behave as a diffusion controlled process. The thickness of Ti layer and the annealing procedure have important effect on CoSi2 epitaxial growth.