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The charging behavior of electric vehicle users is highly stochastic, which makes the short-term prediction of charging load at electric vehicle charging stations difficult. In this paper, a data-driven hybrid model optimized by the improved dung beetle optimization algorithm (IDBO) is proposed to address the problem of the low accuracy of short-term prediction. Firstly, the charging station data are preprocessed to obtain clear and organized load data, and the input feature matrix is constructed using factors such as temperature, date type, and holidays. Secondly, the optimal CNN-BiLSTM model is constructed using convolutional neural network (CNN) and Bi-directional Long Short-Term Memory (BiLSTM), which realizes the feature extraction of the input matrix and better captures the hidden patterns and regularities in it. Then, methods such as Bernoulli mapping are used to improve the DBO algorithm and its hyperparameters; for example, hidden neurons of the hybrid model are tuned to further improve the model prediction accuracy. Finally, a simulation experiment platform is established based on MATLAB R2023a to validate the example calculations on the historical data of EV charging stations in the public dataset of ANN-DATA, and comparative analyses are carried out. The results show that compared with the traditional models such as CNN, BiLSTM and PSO-CNN-BiLSTM, the coefficient of determination of the model exceeds 0.8921 and the root mean square error is maintained at about 4.413 on both the training and test sets, which proves its effectiveness and stability. [ABSTRACT FROM AUTHOR]

In this paper, the projective synchronization problem of nonautonomous neural networks with time delay and Caputo derivative is researched. First, by introducing time delay and variable coefficient into the known neural network model, the neural network that can more accurately describe the interaction between neurons is given. Second, based on the improved neural network model, two global synchronization schemes are achieved, respectively. Finally, by constructing two novel Lyapunov functions and utilizing the properties of delay fractional-order differential inequalities, the asymptotic stability of the zero equilibrium point of the error system obtained from the master–slave systems is proved by some new developing analysis methods, respectively, and some criteria for global projective synchronization of delayed nonautonomous neural networks with Caputo derivatives are obtained, respectively, under two new synchronous controllers. In addition, the correctness of the theoretical results obtained in this paper is verified by some numerical simulation. [ABSTRACT FROM AUTHOR]

Liquid crystal droplets are of great interest from physics and applications. Rigorous mathematical analysis is challenging as the problem involves harmonic maps (or Oseen‐Frank energy minimizers in general), free interfaces, and topological defects which could be either inside the droplet or on its surface along with some intriguing boundary anchoring conditions for the orientation configurations. In this paper, through a study of the phase transition between the isotropic and nematic states of liquid crystal based on the Ericksen model, we can show, when the size of a droplet is much larger in comparison with the ratio of the Frank constants to the surface tension, a Γ‐convergence theorem for minimizers. This Γ‐limit is in fact the sharp interface limit for the phase transition between the isotropic and nematic regions when the small parameter ε, corresponding to the transition layer width, goes to 0. This limiting process not only provides a geometric description of the shape of the droplet as one would expect, and surprisingly it also gives the anchoring conditions for the orientations of liquid crystals on the surface of the droplet depending on material constants. In particular, homeotropic, tangential, and even free boundary conditions as assumed in earlier phenomenological modelings arise naturally, provided the surface tension, Frank‐Ericksen constants are in suitable ranges. © 2022 Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

We establish an optimal L p -regularity theory for solutions to fourth order elliptic systems with antisymmetric potentials in all supercritical dimensions n ≥ 5 : Δ 2 u = Δ (D · ∇ u) + div (E · ∇ u) + (Δ Ω + G) · ∇ u + f in B n , where Ω ∈ W 1 , 2 (B n , s o m) is antisymmetric and f ∈ L p (B n) , and D , E , Ω , G satisfy the growth condition (GC-4), under the smallness condition of a critical scale invariant norm of ∇ u and ∇ 2 u . This system was brought into lights from the study of regularity of (stationary) biharmonic maps between manifolds by Lamm–Rivière, Struwe, and Wang. In particular, our results improve Struwe's Hölder regularity theorem to any Hölder exponent α ∈ (0 , 1) when f ≡ 0 , and have applications to both approximate biharmonic maps and heat flow of biharmonic maps. As a by-product of our techniques, we also partially extend the L p -regularity theory of approximate harmonic maps by Moser to Rivière-Struwe's second order elliptic systems with antisymmetric potentials under the growth condition (GC-2) in all dimensions n ≥ 2 when p > n 2 , which partially confirms an interesting expectation by Sharp. [ABSTRACT FROM AUTHOR]

This study delves into the complexities of frost formation on road surfaces, a phenomenon that presents significant safety hazards in transportation due to its sudden emergence and unpredictable nature. Despite advanced meteorological warning systems for snowfall and freezing rain, black ice and frost remain difficult to predict and counteract. To address this, a controlled indoor simulation experiment was designed to investigate the characteristics of road surface frosting at low temperatures. Results from the experiment indicated that growth of the frost layer thickness follows a parabolic trend with extended freezing time yet the mass of the frost layer increases at a roughly linear rate. The data also revealed that lower temperatures expedite the phase transition of water vapor to ice, leading to faster increases in frost layer height. Additionally, the effects of air temperature and velocity on frost properties were examined. Interestingly, higher air temperatures facilitated rapid frost formation initially, but later stages displayed a plateau phase in the rate of accumulation. Furthermore, increased air velocity up to 1 m/s resulted in greater frost mass, but higher velocities diminished frost formation due to enhanced heat transfer. In conclusion, this study offers a detailed analysis of frost layer development under controlled conditions, providing valuable insights into the environmental factors influencing this hazardous phenomenon. The findings contribute to the understanding of frost dynamics on road surfaces, with implications for improving predictive models and developing effective countermeasures for road safety during icy conditions. • An indoor simulation experiment reveals the parabolic growth of road surface frost layer thickness and a roughly linear increase in mass over time. • Lower temperatures significantly expedite the phase transition from water vapor to ice, hastening the vertical growth of frost layers on road surfaces. • Air temperature and velocity are found to have a nuanced effect on frost formation, with higher temperatures initially promoting rapid accumulation. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to study the following fuzzy system: x n + 1 = A x n − 1 x n − 2 + B x n − 3 D + C x n − 4 ,   n = 0 , 1 , 2 , ⋯ , where { x n } is a sequence of positive fuzzy numbers and the initial conditions x − 4 , x − 3 , x − 2 , x − 1 , x 0 and the parameters A , B , C , D are positive fuzzy numbers. Firstly, the existence and uniqueness of positive fuzzy solutions of the fuzzy system are proved. Secondly, the dynamic behavior of the equilibrium points for the fuzzy system are studied by means of the fuzzy sets theory, linearization method and mathematical induction. Finally, the results obtained in this paper are simulated by using the software package MATLAB 2016, and the numerical results not only show the dynamic behavior of the solutions for the fuzzy system, but also verify the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, we consider weak solutions of the Euler–Lagrange equation to a variational energy functional modeling the geometrically nonlinear Cosserat micropolar elasticity of continua in dimension three, which is a system coupling between the Poisson equation and the equation of |$p$| -harmonic maps (⁠|$2\le p\le 3$|⁠). We show that if a weak solution is stationary, then its singular set is discrete for |$2

Background: Owing to their excellent resistance to abiotic and biotic stress, Thinopyrum intermedium (2n = 6x = 42, JJJsJsStSt) and Th. ponticum (2n = 10x = 70) are both widely utilized in wheat germplasm innovation programs. Disomic substitution lines (DSLs) carrying one pair of alien chromosomes are valuable bridge materials for transmission of novel genes, fluorescence in situ hybridization (FISH) karyotype construction and specific molecular marker development. Results: Six wheat–Thinopyrum DSLs derived from crosses between Abbondanza nullisomic lines (2n = 40) and two octoploid Trititrigia lines (2n = 8x = 56), were characterized by sequential FISH–genome in situ hybridization (GISH), multicolor GISH (mc-GISH), and an analysis of the wheat 15 K SNP array combined with molecular marker selection. ES-9 (DS2St (2A)) and ES-10 (DS3St (3D)) are wheat–Th. ponticum DSLs, while ES-23 (DS2St (2A)), ES-24 (DS3St (3D)), ES-25(DS2St (2B)), and ES-26 (DS2St (2D)) are wheat–Th. intermedium DSLs. ES-9, ES-23, ES-25 and ES-26 conferred high thousand-kernel weight and stripe rust resistance at adult stages, while ES-10 and ES-24 were highly resistant to stripe rust at all stages. Furthermore, cytological analysis showed that the alien chromosomes belonging to the same homoeologous group (2 or 3) derived from different donors carried the same FISH karyotype and could form a bivalent. Based on specific-locus amplified fragment sequencing (SLAF-seq), two 2St-chromosome-specific markers (PTH-005 and PTH-013) and two 3St-chromosome-specific markers (PTH-113 and PTH-135) were developed. Conclusions: The six wheat–Thinopyrum DSLs conferring stripe rust resistance can be used as bridging parents for transmission of valuable resistance genes. The utility of PTH-113 and PTH-135 in a BC1F2 population showed that the newly developed markers could be useful tools for efficient identification of St chromosomes in a common wheat background. [ABSTRACT FROM AUTHOR]

In this paper, we will establish the global existence of a suitable weak solution to the Erickson–Leslie system modelling hydrodynamics of nematic liquid crystal flows with kinematic transports for molecules of various shapes in , which is smooth away from a closed set of (parabolic) Hausdorff dimension at most. [ABSTRACT FROM AUTHOR]

For any n ≥ 2 , Ω ⊂ R n , and any given convex and coercive Hamiltonian function H ∈ C 0 (R n) , we find an optimal sufficient condition on H , that is, for any c ∈ R , the level set H − 1 (c) does not contain any line segment, such then any absolute minimizer u ∈ A M H (Ω) enjoys the linear approximation property. As consequences, we show that when n = 2 , if u ∈ A M H (Ω) then u ∈ C 1 ; and if u ∈ A M H (R 2) satisfies a linear growth at the infinity, then u is a linear function on R 2. In particular, if H is a strictly convex Banach norm ‖ ⋅ ‖ on R 2 , e.g. the l α -norm for 1 < α < ∞ , then any u ∈ A M H (Ω) is C 1. The ideas of proof are, instead of PDE approaches, purely variational and geometric. [ABSTRACT FROM AUTHOR]

In this paper, we consider the boundary value problem of a simplified Ericksen–Leslie system in dimension two with non-slip boundary condition for the velocity field u and time-dependent boundary condition for the director field d of unit length. For such a system, we first establish the existence of a global weak solution that is smooth away from finitely many singular times, then establish the existence of a unique global strong solution that is smooth for t > 0 under the assumption that the image of boundary data is contained in the hemisphere S + 2 . Finally, we apply these theorems to the problem of optimal boundary control of the simplified Ericksen–Leslie system and show both the existence and a necessary condition of an optimal boundary control. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the dynamical behaviour of a class of three species Lotka–Volterra competitive-competitive–cooperative models with feedback controls and time delays. By developing a new analysis technique, we obtain some sufficient conditions that ensure these models have the dynamical property of permanence. We also give some sufficient conditions that guarantee the global attractivity of positive solutions for this system by constructing a new suitable Lyapunov function. Finally, we give some numerical simulations to illustrate our results in this paper. [ABSTRACT FROM AUTHOR]

Distant hybridizations are important for developing common wheat germplasm. Thinopyrum ponticum (2n = 10x = 70), which is a wild relative of wheat, has numerous advantages for enhancing the tolerance of plants to biotic and abiotic stresses. ES-11 and ES-12 are two stable lines derived from a cross between the Triticum aestivum–Th. ponticum partial amphiploid line Xiaoyan784 (2n = 8x = 56) and the wheat Abbondanza nullisomic lines (2n = 40) involving consecutive self-crosses and cytological marker-assisted selection. Lines ES-11 and ES-12 were characterized by a cytogenetic analysis, a sequential fluorescence in situ hybridization (FISH)–genomic in situ hybridization (GISH), and a multicolor GISH (mc-GISH) combined with an analysis of functional molecular markers. Moreover, their agronomic traits and disease resistance were evaluated. The cytogenetic results suggested that ES-11 and ES-12 contained 42 chromosomes. In ES-12, wheat chromosome 3D was replaced by a pair of Th. ponticum 3St chromosomes for a genome composition of 14A + 14B + 12D + 2(3St). In ES-11, wheat chromosome 3B and 4D were replaced by chromosomes 3St and 4 J, respectively, for a genome composition of 14A + 12B + 12D + 2(3St) +2(4J). The detected recombination between chromosomes 3St and 4J and the structural variation of chromosome 2A were due to the introduction of two pairs of Th. ponticum chromosomes. Additionally, ES-11 and ES-12 were resistant to stripe rust at the seedling and adult stages. Thus, the highly disease-resistant wheat–Th. ponticum disomic substitution line (ES-12) and double substitution line (ES-11) are potentially useful germplasms for breeding disease-resistant wheat lines. [ABSTRACT FROM AUTHOR]

This is in the sequel of authors' paper [Lin, F. H., Pan, X. B. and Wang, C. Y., Phase transition for potentials of high dimensional wells, Comm. Pure Appl. Math., 65(6), 2012, 833-888] in which the authors had set up a program to verify rigorously some formal statements associated with the multiple component phase transitions with higher dimensional wells. The main goal here is to establish a regularity theory for minimizing maps with a rather non-standard boundary condition at the sharp interface of the transition. The authors also present a proof, under simplified geometric assumptions, of existence of local smooth gradient flows under such constraints on interfaces which are in the motion by the mean-curvature. In a forthcoming paper, a general theory for such gradient flows and its relation to Keller-Rubinstein-Sternberg's work (in 1989) on the fast reaction, slow diffusion and motion by the mean curvature would be addressed. [ABSTRACT FROM AUTHOR]

In this paper, we obtain optimal time-decay rates in L r (R + 3) for r ≥ 1 of global strong solutions to the nematic liquid crystal flows in R + 3 , provided the initial data has small L 3 (R + 3) -norm. [ABSTRACT FROM AUTHOR]

In this article, we will study the bubbling phenomena of approximate harmonic maps in dimension 2 that have either (i) bounded |$L^2$| -tension fields under the weak anchoring condition, or (ii) bounded |$L\log L \cap M^{1,\delta}$| -tension fields under the strong anchoring condition. [ABSTRACT FROM AUTHOR]

In this paper, a class of three-species multi-delay Lotka–Volterra ratio-dependent predator–prey model with feedback controls and shelter for the prey is considered. A set of easily verifiable sufficient conditions which guarantees the permanence of the system and the global attractivity of positive solution for the predator–prey system are established by developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function. Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In addition, some numerical solutions of the equations describing the system are given to show that the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator–prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system. At the same time, the influence of the delays and shelters on the dynamics behavior of the system is also considered by solving numerically the predator–prey models. [ABSTRACT FROM AUTHOR]

Abstract We investigated the role of a disintegrin and metalloproteinase 17 (ADAM17) in chemo resistance, and to clarify the mechanism underlying reverse of L-OHP resistance by knockdown of ADAM17. CRC tissues with corresponding adjacent normal tissues were collected. The mRNA and protein expression of ADAM17 in tissues were detected by RT-qPCR, immunohistochemistry and Western blot. The prognostic impact of ADAM17 expression were then validated in TCGA database to confirm the results. Resistance to oxaliplatin was induced in HCT-8 (HCT-8/L-OHP) colorectal cancer cell line by exposing cell to increasing concentrations of L-OHP. MTT were used to evaluate the resistance to L-OHP. Subsequently, Knockdown of ADAM17 in HCT-8 and HCT-8/L-OHP cells to explore the mechanism through which ADAM17 shRNA reverses L-OHP resistance. Our result showed that ADAM17 was higher expression in the cancerous tissue and related to the chemosensitivity. Moreover, ADAM17 shRNA, AG1478 and LY294002 could inhibit cell proliferation, induce apoptosis and increase oxaliplatin sensitivity in HCT-8/L-OHP and parental colorectal cancer cell line, but nonsense shRNA did not show this effect. Western blot analysis further confirmed that EGFR/PI3K/AKT signaling pathway is involved in ADAM17 shRNA inhibiting proliferation and chemosensitivity of HCT-8/L-OHP and HCT-8 cells. The present study provides the evidence that downregulation of ADAM17 could increase the sensitivity to chemotherapy, inhibit cell proliferation, induce apoptosis, and reverse oxaliplatin resistance via suppression of the EGFR/PI3K/AKT signaling pathway in CRC. Highlights • High expression of ADAM17 is associated with oxaliplatin chemosensitivity. • Chronic oxaliplatin exposure established drug-resistant cell line HCT-8/L-OHP. • Down regulation of ADAM17 can enhance sensitivity and reverse resistance to oxaliplatin. • Downregulation of ADAM17 inhibit cell proliferation, induce apoptosis via EGFR/PI3K/AKT signaling pathway. [ABSTRACT FROM AUTHOR]

We consider the heat flow of Yang–Mills–Higgs functional where the base manifold is a Riemannian surface and the fiber is a compact symplectic manifold. We show that the corresponding Cauchy problem admits a global weak solution for any H 1 -initial data. Moreover, the solution is smooth except for finitely many singularities. We prove an energy identity at finite time singularities and give a description of the asymptotic behavior at time infinity. [ABSTRACT FROM AUTHOR]

For the class of approximate harmonic maps $$u\in W^{1,2}(\Sigma ,N)$$ from a closed Riemmanian surface $$(\Sigma ,g)$$ to a compact Riemannian manifold ( N, h), we show that (i) the so-called energy identity holds for weakly convergent approximate harmonic maps $$\{u_n\}:\Sigma \rightarrow N$$ , with tension fields $$\tau (u_n)$$ bounded in the Morrey space $$M^{1,\delta }(\Sigma )$$ for some $$0\le \delta <2$$ ; and (ii) if an approximate harmonic map u has tension field $$\tau (u)\in L\log L(\Sigma )\cap M^{1,\delta }(\Sigma )$$ for some $$0\le \delta <2$$ , then $$u\in W^{2,1}(\Sigma , N)$$ . Based on these estimates, we further establish the bubble tree convergence, referring to energy identity both $$L^{2,1}$$ of gradients and $$L^1$$ -norm of hessians and the oscillation convergence, for a weakly convergent sequence of approximate harmonic maps $$\{u_n\}$$ , with tension fields $$\tau (u_n)$$ uniformly bounded in $$M^{1,\delta }(\Sigma )$$ for some $$0\le \delta <2$$ and uniformly integrable in $$L\log L(\Sigma )$$ . [ABSTRACT FROM AUTHOR]

We show the everywhere differentiability of viscosity solutions to a class of Aronsson equations in R n for n ≥ 2 , where the coefficient matrices A are assumed to be uniformly elliptic and C 1 , 1 . Our result extends an earlier important theorem by Evans and Smart [18] who have studied the case A = I n which correspond to the ∞-Laplace equation. We also show that every point is a Lebesgue point for the gradient. In the process of proving the results we improve some of the gradient estimates obtained for the infinity harmonic functions. The lack of suitable gradient estimates has been a major obstacle for solving the C 1 , α problem in this setting, and we aim to take a step towards better understanding of this problem, too. A key tool in our approach is to study the problem in a suitable intrinsic geometry induced by the coefficient matrix A . Heuristically, this corresponds to considering the question on a Riemannian manifold whose the metric is given by the matrix A . [ABSTRACT FROM AUTHOR]

For a bounded domain $${U\subset{{\mathbb{R}}^n}}$$ , consider the $${L^\infty}$$ -functional involving a non-negative Hamilton function $${H:{\overline{U}}\times{{\mathbb{R}}^n}\to [0,\infty)}$$ . In this paper, we will establish the uniqueness of absolute minimizers $${u\in W^{1,\infty}_{\rm loc}(U)\cap C({\overline{U}})}$$ for $${H}$$ , under the Dirichlet boundary value $${g\in C(\partial U)}$$ , provided that: (A1) $${H}$$ is lower semicontinuous in $${\overline U\times{\mathbb{R}}^n}$$ , and $${H(x,\cdot)}$$ is convex for any $${x\in{\overline{U}}}$$ . (A2) $${ H(x,0)=\min_{p\in {{\mathbb{R}}^n}}H(x,p)=0}$$ for any $${ x\in {\overline{U}}}$$ , and $${\bigcup_{x\in \overline U}\{p: H(x,p)=0\}}$$ is contained in a hyperplane of $${{\mathbb{R}}^n}$$ . (A3) For any $${\lambda > 0}$$ , there exist $${ 0 < r_\lambda\leq R_\lambda < \infty}$$ , with $${\lim_{\lambda\to\infty}r_\lambda=\infty}$$ , such that This generalizes the uniqueness theorem by Jensen (Arch Ration Mech Anal 123:51-74, 1993), Jensen et al. (Arch Ration Mech Anal 190:347-370, 2008), Armstrong et al. (Arch Ration Mech Anal 200:405-443, 2011) and Koskela et al. (Arch Ration Mech Anal 214:99-142, 2014) to a large class of Hamiltonian functions $${H(x,p)}$$ with $${x}$$ -dependence. As a corollary, we confirm an open question on the uniqueness of absolute minimizers posed by Jensen et al. (Arch Ration Mech Anal 190:347-370, 2008). The proofs rely on the geometric structure of the action function $${{\mathcal{L}}_t(x,y)}$$ induced by $${H}$$ , and the identification of the absolute subminimality of $${u}$$ with convexity of the Hamilton-Jacobi flow $${t\mapsto T^t u(x)}$$ . [ABSTRACT FROM AUTHOR]

We developed a new disomic addition line M11028-1-1-5 (2n = 44 = 21' + 1') from a cross between wheat cv. '7182' and octoploid Tritileymus M47 (2 n = 8 x = 56, AABBDDN sNs). Cytological observations demonstrated that M11028-1-1-5 contained 44 chromosomes and formed 22 bivalents during meiotic metaphase I. The genomic in situ hybridization ( GISH) investigations showed this line contained 42 wheat chromosomes and a pair of L. mollis chromosomes. SSR, EST and PCR-based landmark unique gene ( PLUG) markers were screened to determine the homoeologous relationships of the introduced L. mollis chromosomes in wheat background. Nine markers, i.e. Xwmc256, Xgpw312, Swes123, CD452568, BF483643, BQ169205, TNAC1748, TNAC1751 and TNAC1752, all of which were located on the homoeologous group 6 chromosomes of common wheat, amplified bands unique to L. mollis in M11028-1-1-5. Gliadin analysis also confirmed that the added chromosomes in M11028-1-1-5 were correlated with the sixth group chromosome. This indicated that M11028-1-1-5 contained a pair of introduced L. mollis chromosome belonging to homoeologous group 6, which we designated it as Lm#6 Ns disomic addition line. This is the first report of a common wheat- L. mollis disomic addition line. [ABSTRACT FROM AUTHOR]

In this study, we developed a method to quantify and link the toxic effects in community-level ecosystems with concentrations of petroleum hydrocarbons. The densities of Platymonas helgolandica var. tsingtaoensis , Isochrysis galbana , and Brachionus plicatilis in single-species tests and customized ecosystems were examined in response to a concentration gradient of petroleum hydrocarbons ranging from 0 to 8.0 mg L − 1 . A three-population ecological model with interspecies competition-grazing relationships was used to characterize population sizes with concentrations of petroleum hydrocarbons. A threshold concentration of the simplified plankton ecosystem of 0.376 mg L − 1 for petroleum hydrocarbons was calculated from the proposed model, which was higher than the no-effect concentration of 0.056 mg L − 1 derived from the single-species toxicity tests and the predicted no-effect concentration of 0.076 mg L − 1 calculated from the species sensitivity distribution. This finding indicates that interspecies competition and grazing reduced the toxic effect of petroleum hydrocarbons at the community level. The sensitivity analysis for model parameters demonstrates that plankton population biomasses are highly sensitive to filtration rates. Antagonism between interspecies interactions and petroleum hydrocarbon toxicity was attributed to the reduced filtration rate and zooplankton grazing pressure. The proposed method is a simple means to address the concern regarding the impacts of ecological interactions on ecological risk assessments of pollutants. [ABSTRACT FROM AUTHOR]

Alien addition lines are important for transferring useful genes from alien species into common wheat. Rye is an important and valuable gene resource for improving wheat disease resistance, yield, and environment adaptation. A new wheat-rye addition line, N9436B, was developed from the progeny of the cross of common wheat ( Triticum aestivum L., 2 n = 6 x = 42, AABBDD) cultivar Shaanmai 611 and rye ( Secale cereal L., 2 n = 2 x = 14, RR) accession Austrian rye. We characterized this new line by cytology, genomic in situ hybridization (GISH), fluorescence in situ hybridization (FISH), molecular markers, and disease resistance screening. N9436B was stable in morphology and cytology, with a chromosome composition of 2 n = 42 + 2t = 22II. GISH investigations showed that this line contained two rye chromosomes. GISH, FISH, and molecular maker identification suggested that the introduced R chromosome and the missing wheat chromosome arms were 1R chromosome and 2DL chromosome arm, respectively. N9436B exhibited 30-37 spikelets per spike and a high level of resistance to powdery mildew ( Blumeria graminis f. sp. tritici, Bgt) isolate E09 at the seedling stage. N9436B was cytologically stable, had the trait of multiple spikelets, and was resistant to powdery mildew; this line should thus be useful in wheat improvement. [ABSTRACT FROM AUTHOR]

Powdery mildew of wheat ( Triticum aestivum L.) caused by Blumeria graminis f. sp. tritici, is a major fungal disease in many areas of the world. Synthetic hexaploids, created from durum wheat and Aegilops tauschii are important sources of beneficial genes for wheat improvement. Synthetic wheat 'SE5785' was found resistant to powdery mildew at the seedling and adult stages. Genetic analyses of the F population and F families developed from a cross of 'SE5785' with the susceptible common wheat, 'Xiaoyan 22', revealed that resistance in 'SE5785' was controlled by a single recessive gene. Bulked segregant analysis was used to map the powdery mildew resistance locus. The resulting genetic map comprised of markers Xcfd62, Xbarc59, PmSE5785, Xgwm539, and Xwmc817 spanned 16.3 cM. Markers Xbarc59 and Xgwm539 were tightly linked to the resistance locus at genetic distances of 3.6 and 4.0 cM, respectively. 'Chinese Spring' and its nulli-tetrasomic lines confirmed that PmSE5785 was located on chromosome 2D. Because no gene for powdery mildew resistance had ever been located on this chromosome in the genus Triticum, this must be a new locus, therefore, designated PmSE5785. N07228-1 and N07228-2 with large seeds and powdery mildew resistance were selected from the progeny of the cross 'SE5785'/'Xiaoyan 22'. These new lines can serve as sources of resistance to powdery mildew in wheat breeding. [ABSTRACT FROM AUTHOR]

Leymus mollis (2n = 4x = 28, NsNsXmXm) possesses novel and important genes for resistance against multi-fungal diseases. The development of new wheat—L. mollis introgression lines is of great significance for wheat disease resistance breeding. M11003-3-1-15-8, a novel disomic substitution line of common wheat cv. 7182 –L. mollis, developed and selected from the BC1F5 progeny between wheat cv. 7182 and octoploid Tritileymus M47 (2n = 8x = 56, AABBDDNsNs), was characterized by morphological and cytogenetic identification, analysis of functional molecular markers, genomic in situ hybridization (GISH), sequential fluorescence in situ hybridization (FISH)—genomic in situ hybridization (GISH) and disease resistance evaluation. Cytological observations suggested that M11003-3-1-15-8 contained 42 chromosomes and formed 21 bivalents at meiotic metaphase I. The GISH investigations showed that line contained 40 wheat chromosomes and a pair of L. mollis chromosomes. EST-STS multiple loci markers and PLUG (PCR-based Landmark Unique Gene) markers confirmed that the introduced L. mollis chromosomes belonged to homoeologous group 7, it was designated as Lm#7Ns. While nulli-tetrasomic and sequential FISH-GISH analysis using the oligonucleotide Oligo-pSc119.2 and Oligo-pTa535 as probes revealed that the wheat 7D chromosomes were absent in M11003-3-1-15-8. Therefore, it was deduced that M11003-3-1-15-8 was a wheat–L. mollis Lm#7Ns (7D) disomic substitution line. Field disease resistance demonstrated that the introduced L. mollis chromosomes Lm#7Ns were responsible for the stripe rust resistance at the adult stage. Moreover, M11003-3-1-15-8 had a superior numbers of florets. The novel disomic substitution line M11003-3-1-15-8, could be exploited as an important genetic material in wheat resistance breeding programs and genetic resources. [ABSTRACT FROM AUTHOR]

Leymus mollis (2 n = 4 x = 28, NsNsXmXm) is an important tetraploid species in Leymus (Poaceae: Triticeae) and a useful genetic resource for wheat breeding because of the stress tolerance and disease resistance of this species. The development of Triticum aestivum (common wheat) - L. mollis derivatives with desirable genes will provide valuable bridge materials for wheat improvement, especially regarding powdery mildew resistance genes, which are rarely documented in L. mollis. In the present study, three derivatives of common wheat cultivar 7182 and L. mollis, namely M47, M51, and M42, were subjected to chromosomal characterization via cytogenetic identification, the analysis of molecular markers, and genomic in situ hybridization. These derivatives were all morphologically and cytogenetically stable. M47 was highly resistant to powdery mildew and nearly immune to stripe rust at the adult stage, and the chromosome constitution of this derivative can be expressed as 2 n = 56 = 42T.a + 14L.m (where T.a = T. aestivum chromosomes; L.m = L. mollis chromosomes). Compared to M47, M42 was also resistant to stripe rust but was susceptible to powdery mildew; the chromosome constitution of M42 was 2 n = 54 = 42T.a + 12L.m, in which a pair of homoeologous group 7 L.m chromosomes was eliminated. Finally, M51 was susceptible to powdery mildew and stripe rust and had a chromosome constitution of 2 n = 48 = 42T.a + 6L.m, in which four pairs of L.m chromosomes from homoeologous groups 2, 4, 5, and 7 were eliminated. The differing disease resistances of the three derivatives are discussed in this report in the context of their chromosomal variations; this information can thus contribute to breeding disease resistant wheat with the potential for applying these derivatives as useful bridge materials. [ABSTRACT FROM AUTHOR]

Given a C2$C^2$ family of vector fields X1,...,Xm$X_1,\ldots ,X_m$ which induces a continuous Carnot–Carathéodory distance, we show that any absolute minimizer of a supremal functional defined by a C2$C^2$ quasiconvex Hamiltonian f(x,s,p)$f(x,s,p)$, allowing s$s$‐variable dependence, is a viscosity solution to the Aronsson equation −∑i=1mXi(f(x,u(x),Xu(x)))∂f∂pi(x,u(x),Xu(x))=0,$$\begin{equation*} \hspace*{10pt}-\sum _{i=1}^m X_i(f(x,u(x),Xu(x)))\frac{\partial f}{\partial p_i} (x,u(x),Xu(x))=0,\hspace*{-10pt} \end{equation*}$$ [ABSTRACT FROM AUTHOR]

For any bounded smooth domain [ABSTRACT FROM AUTHOR]

Abstract: In this paper we establish the uniformity property of a simplified Ericksen–Leslie system modelling the hydrodynamics of nematic liquid crystals on the two-dimensional unit sphere , namely the uniform convergence in to a steady state exponentially as t tends to infinity. The main assumption, similar to Topping [15], concerns the equation of liquid crystal director d and states that at infinity time, a weak limit and any bubble ( ) share a common orientation. As a consequence, the uniformity property holds under various types of small initial data. [Copyright &y& Elsevier]

As an important group in Triticum, tetraploid wheat plays a significant role in the research of wheat evolution. Several complete aneuploid sets of common wheat have provided valuable tools for genetic and breeding studies, while similar aneuploids of tetraploid wheat are still not well developed. Here, 12 double ditelosomics developed in Triticum turgidum L. var. durum cultivar DR147 (excluding dDT2B and dDT3A) were reported. Hybrids between DR147 and the original double-ditelosomic dDT2B of Langdon lost vigor and died prematurely after the three-leaf stage; therefore, the dDT2B line was not obtained. The cytogenetic behaviors and phenotypic characteristics of each line were detailedly described. To distinguish the entire chromosome complement of tetraploid wheat, the DR147 karyotype was established by fluorescence in situ hybridization (FISH), using the Aegilops tauschii clone pAsl and the barley clone pHvG38 as probes. FISH using a cereal-specific centromere repeat (6C6) probe suggested that all the lines possessed four telosomes, except for 4AS of double-ditelosomic dDT4A, which carried a small segment of the long arm. On the basis of the idiogram of DR147, these lines were successfully discriminated by FISH using the probes pAsl and pHvG38 and were then accurately designated. [ABSTRACT FROM AUTHOR]

In this paper, we establish the local well-posedness for the Cauchy problem of a simplified version of hydrodynamic flow of nematic liquid crystals in $${\mathbb{R}^3}$$ for any initial data ( u, d) having small $${L^{3}_{\rm uloc}}$$ -norm of $${(u_{0}, \nabla d_{0})}$$. Here $${L^{3}_{\rm uloc}(\mathbb{R}^3)}$$ is the space of uniformly locally L-integrable functions. For any initial data ( u, d) with small $${\|(u_0, \nabla d_0)\|_{L^{3}(\mathbb{R}^3)}}$$, we show that there exists a unique, global solution to the problem under consideration which is smooth for t > 0 and has monotone deceasing L-energy for $${t \geqq 0}$$. [ABSTRACT FROM AUTHOR]

This article summarizes the main extraction methods for sedimentary phosphorus (P) determination. With sequential chemical extractions, P is supposed to be selectively removed from different compounds in the sediments. Extraction schemes using strong acids and alkaline solutions have been tested on different sediments and found not to extract well-defined fractions. In addition, several systematic errors in these schemes have been detected. Thus, these schemes have been modified and simplified accordingly. The Standards Measurements and Testing Program of the European Commission (SMT) method is a popular modification of these extraction schemes, as it is simple to handle, allows laboratories to achieve reproducible results and could provide a useful tool for routine use by water managers. The SEDEX (sequential extraction method) method, another popular modification, is widely applied in biogeochemical research as it can separate authigenic carbonate fluorapatite from fluorapatite. Other chemical extractions using chelating compounds have attempted to extract P bound with iron and calcium in sediments without disturbing clay-bound or organic P, the purpose being to determine the algal-available non-apatite, apatite and organic fractions of sediment P. All extraction procedures still yield operationally defined fractions and cannot be used for identification of discrete P compounds. Future modifications of the extraction scheme should aim to achieve better extraction efficiency and selectivity, simple handling techniques and methods that can prevent the extracted P from being re-adsorbed onto Fe(OOH) and CaCO. [ABSTRACT FROM AUTHOR]

Powdery mildew is one of the most devastating diseases of wheat in areas with cool and maritime climates. Chinese wheat landrace Baihulu confers a high level of resistance against a wide range of Blumeria graminis DC f. sp. tritici ( Bgt) races, especially those currently prevailing in Shaanxi. The objectives of this study were to determine the chromosome bin location of the mlbhl gene from Baihulu and its allelism with Pm24. To investigate the inheritance of powdery mildew resistance and detect adjacent molecular markers, we constructed a segregating population of 301 F plants and corresponding F families derived from Baihulu/Shaanyou 225. Genetic analysis revealed that a single dominant gene was responsible for seedling stage powdery mildew resistance in Baihulu. A genetic map comprising Xgwm106, Xgwm337, Xgwm1675, Xgwm603, Xgwm789, Xbarc229, Xgpw4503, Xcfd72, Xcfd83, Xcfd59, Xcfd19, and mlbhl spanned 28.2 cM on chromosome 1D. Xgwm603/ Xgwm789 and Xbarc229 were flanking markers tightly linked to mlbhl at genetic distances of 1.5 and 1.0 cM, respectively. The mlbhl locus was located in chromosome bin 1DS 0.59-1.00 delimited by the SSR markers Xgwm337 and Xbarc229. When tested with a differential array of 23 Bgt isolates Baihulu displayed a response pattern that was clearly distinguishable from that of Chiyacao and varieties or lines possessing documented Pm genes. Allelism analysis indicated that mlbhl is a new gene, either allelic or closely linked with Pm24. The new gene was designated Pm24b. [ABSTRACT FROM AUTHOR]

Abstract: We consider in dimension four weakly convergent sequences of approximate biharmonic maps to a Riemannian manifold with bi-tension fields bounded in for . We prove an energy identity that accounts for the loss of hessian energies by the sum of hessian energies over finitely many nontrivial biharmonic maps on . As a corollary, we obtain an energy identity for the heat flow of biharmonic maps at time infinity. [Copyright &y& Elsevier]

In this paper, we will consider an optimal shape problem of heat insulation introduced by [D. Bucur, G. Buttazzo and C. Nitsch, Two optimization problems in thermal insulation, Notices Amer. Math. Soc.64 (2017), 8, 830–835]. We will establish the existence of optimal shapes in the class of 푀-uniform domains. We will also show that balls are stable solutions of the optimal heat insulation problem. [ABSTRACT FROM AUTHOR]

In this paper, we establish a blow up criterion for the short time classical solution of the nematic liquid crystal flow, a simplified version of Ericksen–Leslie system modeling the hydrodynamic evolution of nematic liquid crystals, in dimensions two and three. More precisely, 0 < T * < + ∞ is the maximal time interval iff (i) for n = 3, ; and (ii) for n = 2, . [ABSTRACT FROM AUTHOR]

In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at a finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of the velocity gradient and the square of the maximum norm of the gradient of a liquid crystal director field. [ABSTRACT FROM AUTHOR]

Abstract: We study strong solutions of the simplified Ericksen–Leslie system modeling compressible nematic liquid crystal flows in a domain . We first prove the local existence of a unique strong solution provided that the initial data are sufficiently regular and satisfy a natural compatibility condition. The initial density function may vanish on an open subset (i.e., an initial vacuum may exist). We then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities and . [Copyright &y& Elsevier]

We establish both local and global well-posedness of the heat flow of polyharmonic maps from to a compact Riemannian manifold without boundary for initial data with small BMO norms. [ABSTRACT FROM AUTHOR]

We investigate the well-posedness of (1) the heat flow of harmonic maps from $${\mathbb R^n}$$ to a compact Riemannian manifold N without boundary for initial data in BMO; and (2) the hydrodynamic flow ( u, d) of nematic liquid crystals on $${\mathbb R^n}$$ for initial data in BMO × BMO. [ABSTRACT FROM AUTHOR]

For any n-dimensional compact Riemannian manifold ( M, g) without boundary and another compact Riemannian manifold ( N, h), the authors establish the uniqueness of the heat flow of harmonic maps from M to N in the class C([0, T), W). For the hydrodynamic flow ( u, d) of nematic liquid crystals in dimensions n = 2 or 3, it is shown that the uniqueness holds for the class of weak solutions provided either (i) for n = 2, u ∈ L L ∩ L H, ▿ P ∈ L L, and ▿ d ∈ L L ∩ L H; or (ii) for n = 3, u ∈ L L ∩ L H ∩ C ([0, T), L), P ∈ L L, and ▿ d ∈ L L ∩ C ([0, T), L). This answers affirmatively the uniqueness question posed by Lin-Lin-Wang. The proofs are very elementary. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the oscillation of a class of partial functional population model, and some sufficient conditions for all positive solutions of the model to oscillate about the positive equilibrium are obtained. The approach is based on the upper- and lower-solution method of the partial functional differential equations and the oscillation theory of the functional differential equation. Moreover, some numerical simulations are also given to illustrate our results. [Copyright &y& Elsevier]

Abstract: By using the upper- and lower-solution method of partial functional differential equations and the oscillation theory of functional differential equation, the oscillation of a population equation with diffusion and delay is studied and a sufficient condition for all positive solutions of the equation to oscillate about the positive equilibrium is obtained. Finally, a model arising from ecology is given to illustrate the obtained results. [Copyright &y& Elsevier]

Abstract: For a nonnegative, uniformly convex with , if , , is a viscosity solution of the Aronsson equation (1.7), then . This generalizes the -regularity theorem on infinity harmonic functions in by Savin [O. Savin, -regularity for infinity harmonic functions in dimensions two, Arch. Ration. Mech. Anal. 176 (3) (2005) 351–361] to the Aronsson equation. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence and stability time-periodic solutions for a class of coupled parabolic equations with time delay, and time delays may appear in the nonlinear reaction functions. The existence of time-periodic solutions is for a class of locally Lipschitz continuous reaction functions without any quasimonotone requirement. Our approach to the problem is by the method of upper and lower solution and using Schauder fixed point theorem. Some methods for proving the stability of the periodic solution are also given. The results for the general system can be applied to the standard parabolic equations without time delay and corresponding ordinary differential system. Finally, a model arising from chemistry is used to illustrate the obtained results. [Copyright &y& Elsevier]

For $n\ge 5$ and $k\ge 4$, we show that any minimizing biharmonic map from $\Omega\subset \Bbb R^n$ to S k is smooth off a closed set whose Hausdorff dimension is at most n-5. When n = 5 and k = 4, for a parameter $\lambda\in [0,1]$ we introduce a $\lambda$-relaxed energy $\Bbb H_{\lambda}$ of the Hessian energy for maps in $W^{2,2}(\Omega ; S^4)$ so that each minimizer $u_{\lambda}$ of $\Bbb H_{\lambda}$ is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of $\Bbb H_{\lambda}$ for $\lambda \in [0,1)$. [ABSTRACT FROM AUTHOR]