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This paper deals with the coupled fourth-order parabolic equations, subject to Dirichlet or Navier boundary conditions. We combine the generalized potential well method, the concave method, with the auxiliary methods to classify the initial energy about the existence of blow-up solutions and global solutions. Moreover, the decay estimate of global solutions and the bounds of blow-up time and rate are determined, respectively. [ABSTRACT FROM AUTHOR]

Devonian thick–layer dolostone is widely developed in the Shawozi Formation (SWZF) of the Sichuan Basin, however, the properties of the dolomitisation fluid and its genesis require clarification. This study adopted field observations, microscopic identification, and geochemical data analysis methods that major and trace elements, rare–earth element (REE) analyses, carbon and oxygen isotopes based on 31 samples. The results showed that dolomites were divided into crystalline dolomites and calcareous dolomites. Crystalline dolomite, which is the most widely distributed, can be further divided into fine crystalline dolomite (FCD), fine–medium crystalline dolomite (FMCD), medium crystalline dolomite (MCD), and coarse crystalline dolomites (CCD). Calcareous dolomite, fine crystalline dolomite (FCD), and fine–medium crystalline dolomite (FMCD) have higher Fe, higher Mn, and lower Sr, whereas medium crystalline dolomite (MCD) and coarse crystalline dolomite (CCD) have the opposite characteristics. The REE content was lower and weak negative anomalies of Ce and Eu were apparent, indicating that dolomite was formed in a fragile redox environment and at a relatively low temperature. The δ13CPDB value had a small variation range, with an average value of 0.04‰. Although the variation range of δ18OPDB value was more extensive, most samples were concentrated in the range of -6.53‰~-2.1‰, indicating that the overall effect of diagenetic alteration was more negligible. Two dolomitisation models were developed: reflux seepage and burial dolomitisation. The reflux seepage model mainly developed calcareous dolomite, whereas the burial model mainly developed crystalline dolomite. The degree of dolomitisation increased with increasing burial depth and formation pressure. [ABSTRACT FROM AUTHOR]

Infrared observation is a crucial tool in the study of astronomical celestial bodies. Metamaterials have a vast prospect for applications in the field of optics due to their unique electromagnetic tunable characteristics. In order to obtain an ultra-broadband high absorption material in the infrared region, we proposed a metal-dielectric-metal-dielectric-metal (MDMDM) metamaterial absorber using a titanium (Ti) nano-cross layer based on surface plasmon polariton (SPP) resonance and magnetic resonance cavity principles. The geometrical parameters of each layer have been examined carefully. The influence of incident angle from 0° to 60° is investigated for transverse electric and transverse magnetic plane-waves. Near-perfect absorption performance is achieved from near-infrared to mid-infrared region. The average absorption reaches as high as 97.41% from 2.05 to 6.08 μm. The absorber exhibits polarization-sensitive characteristics. The absorption peaks are 99.50% and 99.80% at 2.55 and 5.24 μm, respectively. The proposed material has potential applications in astronomical imaging, volcano and fire detection, remote sensing, biological monitoring, and other optical devices. [ABSTRACT FROM AUTHOR]

In this paper, we study blowup properties of weak solutions in their W 1 , ∞ norm to the degenerate parabolic equation with multi-nonlinearities and gradient terms. First, we show the existence and uniqueness of weak solutions by using the priori estimate methods. Second, we obtain the global existence criteria and blowup criteria after proving some gradient estimates for different coefficients. Third, we use some Sobolev's inequalities and deal with some differential inequalities of new barrier functions to determine some upper and lower bounds of blowup time of solutions. It could be found out that the blowup or global existence phenomena depend sensitively on the relationship among the different exponents of nonlinearities, which discover a key clue to the different effect of diffusion, gradient term, source term and absorption term on the singular properties of weak solutions. [ABSTRACT FROM AUTHOR]

This paper deals with a p(x)-Laplacian parabolic problem involving positive and negative sources, subject to a homogeneous Dirichlet boundary condition. We classify the initial energy and the Nehari energy completely to show global existence and blow-up of weak solutions. More- over, we obtain non-extinction and extinction properties of weak solutions. [ABSTRACT FROM AUTHOR]

This paper deals with the fourth‐order parabolic equation ut+Δ2u=μup(x)−λuq(x)$$ {u}_t+{\Delta}^2u=\mu {u}^{p(x)}-\lambda {u}^{q(x)} $$ in a bounded domain, subject to homogeneous Navier boundary conditions. Under some conditions on the variable exponents, we give a complete and optimal classification on the singularity of solutions, characterized by the signs of the Nehari energy and the difference between the initial energy and the potential depth. [ABSTRACT FROM AUTHOR]

This paper deals with the parabolic equations coupled via nonlocal multiple nonlinearity. We determine the critical Fujita exponents for blow-up solutions, which are influenced by the time coefficients. Moreover, we obtain the complete and optimal classification on simultaneous and non-simultaneous blow-up of solutions. Then simultaneous blow-up rates and estimates on blow-up time are studied according to the precise blow-up phenomena for all of the dimensions of the space domain. [ABSTRACT FROM AUTHOR]

Junggar Basin is an important exploration zone for sandstone‐hosted uranium deposits in north‐west China. However, neither the provenance of the host sandstone nor the uranium supply capacity of the potential source rocks have been well evaluated. To determine the provenances of the Mesozoic to Cenozoic sandstone grains and to evaluate relationships between the uranium source and the detritus provenances, a field investigation was performed at the Honggou section in the southern Junggar Basin. U–Pb geochronology and Hf isotopes were obtained from populations of detrital zircons from Jurassic through Palaeogene sandstones. The detrital zircon U–Pb ages display three main groups: 145–190 Ma, 250–360 Ma, and 360–460 Ma. The detrital zircon age distributions and the Hf isotopic characteristics of the sandstones correspond to different igneous rock units within the North and Central Tianshan Mountains. Therefore, the changes in the relative proportions of the zircon age populations indicate that there were major shifts of the provenance areas for the sandstones throughout the Early Jurassic to Palaeogene interval. The majority (92%) of Hf isotope εHf(t) values are positive and in the range of +0.7 to +15.5, which indicates that the majority of the zircons had crystallized in igneous rocks that were mainly derived from juvenile crust or depleted mantle. The majority (93%) of the two‐stage model ages (TDM2) are less than 1.8 Ga, thereby indicating the source of the majority of the igneous rocks was from the melting of ancient Meso‐Proterozoic juvenile crust. Carboniferous–Permian intermediate‐felsic igneous rocks in the Tianshan Mountains may be the primary source of released mobilized uranium and uranium‐enriched siliciclastics into the southern Junggar Basin. This study will assist in future uranium prospecting in this region. [ABSTRACT FROM AUTHOR]

Enamel coating, which is of low thermal conductivity and high chemical stability, has been employed for the protection of many hot parts against oxidation. It is composed of multiple oxides, and each oxide component plays a certain role on thermophysical properties. In this paper, a type of silicate enamel coating with different contents of oxide component Al 2 O 3 was prepared on K444 superalloy. Its microstructural evolution and cyclic oxidation behavior at 1000 °C were investigated. Results indicated that the A0 enamel coating, which was free of Al 2 O 3 in composition, suffered from serious crystallization at high temperature. The formation of quartz, cristobalite and SrSiO 3 crystals resulted in significant mass loss during cyclic oxidation. However, precipitation of these crystals was almost completely prohibited in the A10 and A15 coatings with 10 and 15 wt% Al 2 O 3 , respectively. The A10 coating had no mass loss after cyclic oxidation. But much high content of Al 2 O 3 resulted in the formation of abundant long strip crystals of SrAl 2 Si 2 O 8 in the A15 coating, which led to minor spallation. Furthermore, enamel coatings with Al 2 O 3 (above 6 wt%) promoted the formation of a continuous alumina scale at the enamel/alloy interface, which improved oxidation resistance and increased bonding strength. The well grown alumina scale at interface as well as the mild crystallization ensured high spallation resistance of the enamel coating A10. [ABSTRACT FROM AUTHOR]

Herein, a multicomponent bioactive glass (0Z, 46SiO 2 –30CaO–18Na 2 O–6P 2 O 5 , wt.%) is prepared via melting. ZrO 2 is introduced into the bioglass using two different methods, and then three types of glass-ceramic bulks are manufactured using low-cost pressureless sintering. The effect of ZrO 2 addition on the bioactivity and mechanical properties of the bioactive glass-ceramic is assessed. The results indicate that the main crystalline precipitate from the bioactive glass-ceramic is Na 2 Ca(Si 2 O 6). The crystallisation ability of the 5Z glass-ceramic, bioactive glass-ceramic with ZrO 2 added during melting at high temperature, is reduced because ZrO 2 participated in the reconstruction of the glass network. Further, the ZrO 2 addition led to a low rate of cation release when soaked in simulated body fluid, indicating a decreased bioactivity. At the same time, the 5Y bioactive glass-ceramic, prepared by mixing YSZ particles with 0Z using ball-milling, possesses not only the highest mechanical strength (about twice the strength of 0Z) but also a high bioactivity. This study presents a promising method for the production of excellent bioactive glass-ceramic and a candidate (5Y) for the clinical applications where load bearing is required. [ABSTRACT FROM AUTHOR]

The aging of microplastics (MPs) is extremely influenced by photochemically-produced reactive intermediates (PPRIs), which are mediated by natural photosensitive substances. Algal extracellular polymeric substances (EPS) can produce PPRIs when exposed to sunlight. Nonetheless, the specific role of EPS in the aging process of MPs remains unclear. This work systematically explored the aging process of polystyrene (PS) MPs in the EPS secreted by Chlorella vulgaris under simulated sunlight irradiation. The results revealed that the existence of EPS accelerated the degradation of PS MPs into particles with sizes less than 1 µm, while also facilitating the formation of hydroxy groups on the surface. The release rate of dissolved organic matter (DOM) from PS MPs was elevated from 0.120 mg·L-1·day-1 to 0.577 mg·L-1·day-1. The primary factor contributing to the elevated levels of DOM was humic acid-like compounds generated through the breakdown of PS. EPS accelerated the aging process of PS MPs by primarily mediating the formation of triplet excited states (3EPS*), singlet oxygen (1O 2), and superoxide radicals (O 2 ∙-), resulting in indirect degradation. 3EPS* was found to have the most substantial impact. This study makes a significant contribution to advance understanding of the environmental fate of MPs in aquatic environments impacted by algal blooms. [Display omitted] • Algae EPS greatly enhanced the microplastic (MP) aging under simulated sunlight. • Photoaging of MP induced by EPS led to changes in MP physicochemical properties. • 3EPS*, 1O 2 , and O 2 ∙- mediated by EPS contributed to the MP aging. • 3EPS* was the dominant specie for accelerating the aging process of MPs. [ABSTRACT FROM AUTHOR]

The coal‐bearing Yan'an Formation in the Ordos Basin of the Middle Jurassic was deposited in a river delta–lacustrine sedimentary environment with relatively stable accumulation rates. Spectral analysis and wavelet transform analysis of the natural gamma‐ray (GR) curves from several boreholes through the Yan'an Formation yielded five main sedimentary cycles with wavelengths of 34–57, 10–18, 8–14, 2.9–4.1, and 2–3 m. These cycles were controlled by orbital cycles of eccentricity (405, 128, and 97 kyr), obliquity (35 kyr), and precession (22 kyr), and the long‐eccentricity period of 405 kyr was the most significant cycle. Filtering the sedimentary records for the long‐wavelength cycle and short‐wavelength cycle implies that there are 11 long‐eccentricity cycles and 35 short‐eccentricity cycles preserved in the Yan'an Formation. Assigning the 405 kyr long‐eccentricity cycle to the filtered 11 primary long‐wavelength cycles implies that the Yan'an Formation spanned 4.4 Myr. The orbital–climate cycles were critical factors in the sediment facies changes and episodes of coal formation within the basin. The long‐eccentricity cycles of the Milankovitch cycle are the predominant control factors of the coal seams deposited in the Middle Jurassic Yan'an Formation. [ABSTRACT FROM AUTHOR]

Background: Montreal Cognitive Assessment (MoCA) and Mini-Mental State Examination (MMSE) are neuropsychological tests commonly used by physicians for screening cognitive dysfunction of Alzheimer's disease (AD). Due to different imperfect reference standards, the performance of MoCA and MMSE do not reach consensus. It is necessary to evaluate the consistence and differentiation of MoCA and MMSE in the absence of a gold standard for AD.Objective: We aimed to assess the accuracy of MoCA and MMSE in screening AD without a gold standard reference test.Methods: Studies were identified from PubMed, Web of Science, CNKI, Chinese Wanfang Database, China Science and Technology Journal Database, and Cochrane Library. Our search was limited to studies published in English and Chinese before August 2021. A hierarchical Bayesian latent class model was performed in meta-analysis when the gold standard was absent.Results: A total of 67 studies comprising 5,554 individuals evaluated for MoCA and 76,862 for MMSE were included in this meta-analysis. The pooled sensitivity was 0.934 (95% CI 0.905 to 0.954) for MoCA and 0.883 (95% CI 0.859 to 0.903) for MMSE, while the pooled specificity was 0.899 (95% CI 0.859 to 0.928) for MoCA and 0.903 (95% CI 0.879 to 0.923) for MMSE. MoCA was useful to rule out dementia associated with AD with lower negative likelihood ratio (LR-) (0.074, 95% CI 0.051 to 0.108). MoCA showed better performance with higher diagnostic odds ratio (DOR) (124.903, 95% CI 67.459 to 231.260).Conclusion: MoCA had better performance than MMSE in screening dementia associated with AD from patients with mild cognitive impairment or healthy controls. [ABSTRACT FROM AUTHOR]

In order to determine the provenance and variation characteristics of sandstone-type uranium deposits located in the southwest Ordos Basin, U−Pb geochronology and Hf isotope analyses were conducted on detrital zircons from the Late Mesozoic strata of the SD01 well in the Zhenyuan area. The detrital zircon U−Pb ages of four samples exhibited four main peaks at 250–330, 420–500, 1 720–2 000, and 2 340–2 580 Ma, with a small number of zircons dated at 770–1 100 Ma. The detrital zircon age spectrum and further restriction provided by the in-situ Hf isotopic data suggest that the provenance of each stratum was mainly derived from the crystalline basement rock series (Khondalites, intermediate-acidic intrusive rocks, and metamorphic rocks) of the Alxa Block to the northwest and the Yinshan Block to the north, with minor amounts of Caledonian magmatic rocks and Jingning Period rocks from the western part of the northern Qilian orogenic belt to the west and the northern Qinling orogenic belt to the south. The provenance of the sandbody has not changed significantly and is of the Middle Jurassic-Early Cretaceous. The clear variations in the zircon ages of the samples from the Zhiluo and Anding formations were likely influenced by climate change during the Middle-Late Jurassic. The Triassic zircon age (<250 Ma) first appeared in Early Cretaceous strata, suggesting that tectonic activity was relatively strong in the northern Qinling orogenic belt during the Late Jurassic and produced extensive outcrops of Indo-Chinese granite, which were a source of basin sediments. [ABSTRACT FROM AUTHOR]

This paper deals with qualitative properties of solutions in a parabolic equation with nonstandard growth conditions and singular medium void. For the sublinear source, we prove that all solutions are global. For the linear source, the solutions are global provided that the measure of domain is small. For the superlinear source, the solutions blow up at infinite time given the initial data belonging to the unstable set, and blow up in finite time with positive or negative energy, respectively. The exponential decay rates of global solutions are demonstrated as well and the bounds of blow-up time are determined for all dimensions of space domain. At last, we discuss the blow-up rates of solutions. [ABSTRACT FROM AUTHOR]

Purpose: This paper propose an algorithm for the multiple silicon steel coils multiperiod two-dimensional lengthwise cutting stock problem (m2DLCSP), so as to minimize the total cost of materials and production. Design/methodology/approach: The authors propose a sequential leftovers utilization correction (SLUC) algorithm for the m2DLCSP. The algorithm primarily considers three optimization strategies. First, it considers usable leftovers to simplify the cutting process and improve material utilization. The total quantity and types of leftovers should be limited in order to avoid leftover overstock. Second, it uses a splice method of items to improve the generated cutting plan. Third, it takes into account operational restrictions in the cutting operations. Operational restrictions include imposing maximum and minimum lengths on the cutting patterns, and the limitation of cutting knives at the slitting machines. Findings: Several sets of benchmark with real-world and randomly generated instances are provided to evaluate the algorithm. Compared with literature algorithm and current procedure applied in enterprises, the computational results indicate that proposed algorithm can effectively reduce the total cost, and the computation time is reasonable for practical use. Social implications: This algorithm can effectively reduce the total cost. Originality/value: The proposed method can effectively applied to solve the m2DLCSP and improve the economic efficiency of enterprises. [ABSTRACT FROM AUTHOR]

This paper deals with a homogeneous Dirichlet initial-boundary value problem of the Kirchhoff equation of pseudo-parabolic type with logarithmic nonlinearity, ut-Δut-M(‖∇u‖22)Δu=|u|q-2ulog|u|,(x,t)∈Ω×(0,T),\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\begin{aligned} u_{t}-\Delta u_t-M(\Vert \nabla u\Vert _2^{2})\Delta u=|u|^{q-2}u \,{\log }|u|, \ (x,t) \in \Omega \times (0,T), \end{aligned}$$\end{document}where M(s):=a+bs\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$M(s):=a+bs$$\end{document}, a,b>0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$a,b>0$$\end{document}, q>2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$q>2$$\end{document}; Ω⊂RN\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Omega \subset \mathbb {R}^N$$\end{document} is a bounded domain with Lipschitz boundary. Firstly, we employ the extended Galerkin method to prove the local existence and uniqueness of weak solution. Secondly, for q>4\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$q>4$$\end{document}, we show the criteria on the existence of blow-up solutions or global solutions, which depend on the choosing of the initial energy and Nehari energy. Thirdly, for q+μ≤4\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$q+\mu \le 4$$\end{document}, we give the results on global solutions and large time estimate, where μ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mu $$\end{document} is a positive constant. [ABSTRACT FROM AUTHOR]

This paper deals with homogeneous Dirichlet problems of localized parabolic equations with different diffusion, where reaction terms are the product of the three components of solutions. According to the nontrivial coupled relationship, different non-simultaneous and simultaneous blow-up criteria are proposed for the three components. Then we show non-simultaneous blow-up profile and boundary layer estimates of solutions with or without standard growth conditions on the localized sources near blow-up time. [ABSTRACT FROM AUTHOR]

In this paper, we study the reaction–diffusion equations with variable coefficients in some bounded domains. At least one of the components of solutions blows up for every initial data in some exponent regions, where the Fujita exponents are determined by the exponents of the sources and the coefficients and the dimension of the domain. We also show the classifications of simultaneous and nonsimultaneous blow-up of the components of solutions. The asymptotic properties are discussed including blow-up rates and sets. Moreover, the upper and the lower bounds of blow-up time are given for all dimensions of domains, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we consider the time-weighted parabolic equations in a bounded domain, subject to homogeneous Dirichlet boundary conditions. First, we determine the critical Fujita exponents of solutions prescribed by the coefficients of weighted functions and the first eigenvalue of Laplacian operator with zero Dirichlet boundary. Second, we distinguish completely simultaneous blow-up from non-simultaneous blow-up of two components of solutions. Third, blow-up rates and blow-up time estimates are studied according to different blow-up phenomena. It can be found out that the nonlinear functions of the components determine the orders of them. [ABSTRACT FROM AUTHOR]

In the Mogao Grottoes of Dunhuang, China, the ambient relative humidity (RH) fluctuation in the caves is the main cause for the deterioration that has been observed, especially the deterioration of the earthen plaster and wall paintings linked to the presence of NaCl and Na2SO4 salt contaminants. To help identify the mechanism responsible for this salt-related deterioration and provide a theoretical basis for the development of a preventive conservation regime, this study addressed the basic moisture adsorption mechanisms of earthen plaster with soluble salts by taking an experimental approach. It is shown that, as ambient RH increases, the moisture adsorption process of the plaster containing the soluble salts can be regarded to have three basic stages, as evidenced by the results of the moisture adsorption tests performed on earthen plaster samples with different NaCl or Na2SO4 contents at various humidity levels. The moisture adsorption mechanism and its determining factors at each stage are also analysed. In addition, it is suggested that the hygroscopicity of the plaster structure and the interaction between the different kinds of salts in the plaster, which makes the dissolution or hydration of the salt in the plaster pores much easier, should be considered more seriously regarding increases in the ambient RH in the caves. [ABSTRACT FROM AUTHOR]

Backgrounds/Aims: Ovarian cancer is the most lethal gynaecologic malignancy and is difficult to detect early. The inefficient early diagnosis of ovarian cancer is the main contributor to its high mortality rate. Aptamers, as chemical antibodies, are single-stranded DNA or RNA oligonucleotides that target cells or molecules with high affinity. Methods: Binding ability of R13 was measured by flow cytometry analysis. Stability of R13 was tested in blood serum of an ovarian cancer patient. Internalization of R13 was verified by confocal microscope imaging. 80 cases ovarian cancer tissues, 10 cases normal ovary tissues in a microarray and 6 fallopian tube tissues were prepared for this study. R13's target ability was further confirmed in vivo tumor models in NOD/SCID mice. Results: In this study, we found aptamer R13 bound to ovarian cancer cells with dissociation constants in the nanomolar range. Moreover, these results were further confirmed by tissue imaging. Next we demonstrated that the targets of R13 are membrane proteins and that its internalization occurs in a caveolae-mediated and clathrin-mediated manner. The target function of R13 was determined by imaging A2780 tumours in mouse models. Conclusion: These findings suggest that R13 is a promising novel tool to diagnose and deliver drugs to treat ovarian cancer. [ABSTRACT FROM AUTHOR]

This paper deals with parabolic equations with different diffusion coefficients and coupled nonlinear sources, subject to homogeneous Dirichlet boundary conditions. We give many results about blow-up solutions, including blow-up time estimates for all of the spatial dimensions, the critical non-simultaneous blow-up exponents, uniform blow-up profiles, blow-up sets, and boundary layer with or without standard conditions on nonlocal sources. The conditions are much weaker than the ones for the corresponding results in the previous papers. [ABSTRACT FROM PUBLISHER]

In this paper, we study a free boundary model describing growth of tumors under action of drugs. To our knowledge, in theoretical discussion for free boundary problems, the proliferation rate in tumor models discussed in previous bifurcation results is a linear function of nutrients and inhibitors. Whereas in this paper we consider the net proliferation rate as a nonlinear function depending on both nutrients and drugs. First, the existence and the uniqueness of radially symmetric stationary solutions are obtained. Second, we prove that symmetry-breaking solutions bifurcate from the radially symmetric stationary solutions when the concentration of drug on the boundary of tumor is less than one in the rescaled model. [ABSTRACT FROM AUTHOR]

The Callovian–Oxfordian carbonates in the northeastern Amu Darya Basin of southeastern Turkmenistan, are composed of medium-to thick-bedded, mostly grainy limestones with various skeletal (bivalves, brachiopods, echinoderms, foraminifera, corals, and sponge) and non-skeletal grains (intraclasts, ooids, and peloids). The 6 microfacies types recognized in the Callovianand and 18 microfacies types in Oxfordian carbonates are grouped into two depositional phases, ramp and platform. The Callovian carbonates were deposited on a carbonate ramp, which evolved into a depositional platform in the Oxfordian. The main components of the Oxfordian platform margin complex are reefs and shoals. The principal reef builders are corals, algae and sponges. Regional tectonic movements, eustatic sea-level changes and sedimentation rates were the primary controlling factors of facies evolution during the Callovian–Oxfordian time in the northeastern Amu Darya Basin. [ABSTRACT FROM AUTHOR]

This paper deals with asymptotic behavior for blow-up solutions to time-weighted reaction-diffusion equations u t=Δ u+ e α t v p and v t=Δ v+ e β t u q, subject to homogeneous Dirichlet boundary. The time-weighted blow-up rates are defined and obtained by ways of the scaling or auxiliary-function methods for all α [ABSTRACT FROM AUTHOR]

This paper considers both quenching and blowup phenomena to the coupled parabolic equations with zero Dirichlet boundary. Here, one component of the solution represents the density of some chemical and the other denotes its temperature in some ignition process. All the singular phenomena have been obtained including simultaneous and nonsimultaneous blow-up or quenching, which are classified completely by the exponents. The results extend the ones in the previous paper (Liu and Chan, 2011). [ABSTRACT FROM AUTHOR]

This paper deals with simultaneous blow-up solutions to a Dirichlet initial–boundary problem of the parabolic equations u t = div ( a ( x ) ∇ u ) + ∫ Ω u m v s d x and v t = div ( b ( x ) ∇ v ) + ∫ Ω u q v p d x in Ω × [ 0 , T ) . We complete the previous known results by covering the whole range of possible exponents. Then uniform blow-up profile is obtained for all simultaneous blow-up solutions through proving new rules for some auxiliary systems. At last, boundary layer is studied. [ABSTRACT FROM AUTHOR]

The theory of discrete and continuous frames was introduced for the purpose of analyzing and reconstructing signals mainly in Hilbert spaces. However, in many interesting applications the analyzed space is usually a Banach space, and consequently the stable analysis/reconstruction schemes need to be investigated for general Banach spaces. Parallel to discrete Hilbert space frames, the theory of atomic decompositions, p -frames and framings have been introduced in the literature to address this problem. In this paper we focus on continuous frames and continuous framings (alternatively, integral reconstructions) for Banach spaces by the means of g-Köthe function spaces, in which the involved measure space is σ -finite, positive and complete. Necessary and sufficient conditions for a measurable function to be an L ρ -frame are obtained, and we obtain a decomposition result for the analysis operators of continuous frames in terms of simple Köthe–Bochner operators. As a byproduct we show that a Riesz type continuous frame doesn't exist unless the measure space is purely atomic. One of our main results shows that there is an intrinsic connection between continuous framings and g-Köthe function spaces. [ABSTRACT FROM AUTHOR]

Iron oxides play an important role in the transport and transformation of organic phosphorus in aquatic environments. However, the effect of different types of iron oxide on the environmental fate of organic phosphorus has remained unclear. In this study, the photodegradation of the organic phosphorus compound adenosine triphosphate (ATP) via the activity of crystalline (goethite) and amorphous (ferrihydrite) iron oxides was investigated. It was found that ATP was photodegraded by goethite, resulting in the release of dissolved inorganic phosphate under simulated sunlight irradiation. The concentration of ATP on goethite decreased by 75% after 6 h of simulated sunlight irradiation, while the concentration of ATP on ferrihydrite decreased by only 22%. ATR-FTIR spectroscopy revealed that the intensity of the peaks for the P–O and P O stretching vibrations in the goethite−ATP complex decreased significantly more after simulated sunlight irradiation than did those for the ferrihydrite treatment. Combined with the higher TOC/TOC 0 values for the goethite treatment, the results indicate that a more vigorous photochemical reaction took place in the presence of goethite than with ferrihydrite. Reactive oxygen species analysis also showed that hydroxyl and superoxide anion radicals were generated when goethite was exposed to simulated sunlight irradiation, while ferrihydrite did not exhibit this ability. Overall, this study highlights that the type of iron oxide is an important factor in the transformation of organic phosphorus in aquatic environments. [Display omitted] • Transformation of organic phosphorus after adsorption was investigated. • Organic phosphorus adsorbed on goethite underwent photodegradation. • •OH and O 2 •− generated on the gothite, but not ferrihydrite. • Iron minerals mediated the environmental fate of organic phosphorus. [ABSTRACT FROM AUTHOR]

In this article, the measure space associated with a continuous frame is supposed to be σ-finite and positive, and a frame range is the range of the analysis operator for a continuous frame. Gabardo and Han in 2003 asked whether two frame ranges can both be contained in another one. To solve this problem, we give two decompositions of analysis operators and frame ranges for continuous frames respectively, which essentially establish a relationship between continuous frames and Hilbert-Schmidt operator valued frames. As applications, it follows that only separable Hilbert space can have a continuous frame, that there exists a continuous frame of Riesz-type if and only if the associated measure space is purely atomic, and that the sum of two frame ranges is still a frame range when the sum is closed. Finally, we construct a counterexample which shows that the Gabardo-Han problem is not necessarily true in general. [ABSTRACT FROM AUTHOR]

The distinctive features of the Lower Devonian rocks of the Longmenshan area in southwestern China are brachiopod shell concentrations, especially in the Bailiuping, Ganxi and Xiejiawan Formations, where brachiopod shell concentrations occur widely throughout. Depending on the dominant skeletal elements, six types of shell concentrations can be distinguished: Protochonete , Acrospirifer , Howellella , Orientospirifer , polyspecific shell and polyspecific fragments concentrations. According to the shell features, taphonomic signature, host sediments and their relationships, four genetic models of the various shell concentrations are described in this paper. The genetic processes and distributions along an onshore–offshore area were clarified on the base of taphonomic analysis. Pavements of opportunistic species of Protochonetes are autochthonous assemblages living in quieter, deeper, more offshore waters near the maximum storm wave base. The pavements are the result of reduced sedimentation; the substrate was silty and water-saturated with variable turbidity soupy-mud. Transport by high-energy processes is interpreted as the final formation process of polyspecific fragments concentrations with most extensive scope from intertidal zone to the maximum storm wave base. The Acrospirifer , Howellella , and Orientospirifer concentrations have been stirred by storm wave action and quickly buried after short transport tempestite model. They are most easily preserved around the average storm wave-base. The polyspecific shell concentrations, which include large bivalves are autochthonous assemblages living in shallow and relatively quieter water near shore environments. Autochthonous assemblages of the opportunist Protochonetes bailiupingensis occurring in the Bailiuping Formation of the Longmenshan area not only record of storm events, but are also important features to identify and correlate the Bailiuping Formation in the field. [ABSTRACT FROM AUTHOR]

This paper deals with the nonsimultaneous blow-up problems forwith coupled nonlinear boundary flux. The main results extend the existence of two components blowing up simultaneously in the paperJ. Math. Anal. Appl.2009;356:215–231 to the case ofcomponents blowing up simultaneously. We verify that blow-up phenomena are independent of the choosing of the initial data in some exponent regions, while, in some others, the blow-up phenomena depend sensitively on the choosing of initial data. Moreover, the blow-up rates and sets are obtained for blow-up components. [ABSTRACT FROM PUBLISHER]

[Display omitted] • Apatite fission-track analysis indicates a multi-stage exhumation history. • There are four peaks are interpreted as significant regional uplift episodes. • Statistical results suggest close relationship between exhumation and uranium mineralization. • Late Cretaceous–early Paleogene and latest Miocene-Present are main mineralization episodes. The phases of tectonic activity and exhumation of the southern margin of the Junggar Basin during the Cretaceous through Cenozoic shows significant relationships with the timing of uranium mineralization episodes. To clarify the succession of metallogenetic stages that were controlled by different phases of uplift and exhumation, apatite fission track (AFT) thermochronology was performed on the Jurassic through Cenozoic sediments from the Manas section in the southern Junggar Basin. The mean ages of the AFT suites range from 63 Ma to 133 Ma, and are younger than the host sediment for the Mesozoic samples and older than the host for the Cenozoic samples. The mean track lengths (MTLs) are between 10 and 11 μm. These results indicate that most of the apatite grain assemblages in these samples experienced complicated annealing histories. AFT ages were combined with thermal history modeling to unravel the timing of the multi-phase regional uplift and exhumation history and to reveal the tectonic constraints on the uranium mineralization. The populations of AFT single-grain ages display four peaks, which are interpreted as regional uplift and cooling episodes: mid-Early Jurassic (189–180 Ma), late Jurassic–early Cretaceous (157–116 Ma), late Cretaceous–early Paleocene (88–59 Ma) and late Eocene–early Oligocene (37–28 Ma). Thermal history modeling indicates two episodes of rapid cooling of the basin sediment deposits during the late Cretaceous–Paleocene (80–50 Ma) and the Pliocene (5 Ma)–Present. A synthesis of the temporal relationship between AFT age peaks, of the modeled time–temperature paths, of a compilation of age data and regional geologic events from the Tianshan mountain belt, suggests a close relationship between tectonic evolution and uranium mineralization. Uranium metallogenesis episodes occurred in conjunction with tectonic uplift and exhumation episodes along the southern margin of the Junggar Basin during the late Cretaceous–early Paleogene and during the latest Miocene-Present. The earlier episode was the primary mineralization stage, and the later episode was a partial transformation stage superimposed on the earlier one. [ABSTRACT FROM AUTHOR]

During the Cenozoic a typical lacustrine tempestite deposition was developed in the Lulehe and Xichagou sections of the Qaidam Basin. The sedimentary structures of these two sections above are examined here in detail, which consist of storm erosion, storm tear, storm wave and rapid storm-generated sedimentary structures after storm processes, such as groove casts, scour structures, cutoff structures, hummocky cross-stratification (HCS), parallel bedding and graded bedding. On the basis of these sedimentary characteristics and the vertical facies sedimentary sequence, the causes of the sedimentary succession are analyzed and a Cenozoic sedimentary model of the Qaidam Basin containing shallow proximal, transitional and deep distal tempestites is established. According to the tempestite scale and HCS wavelength, the Cenozoic storm was obviously more intense in the basin's Upper Ganchaigou formation than that in the Lower Youshashan formation. This variation indicates that a paleoclimatic transition largely corresponded with the second uplift of the whole Qinghai-Tibet Plateau. The discovery of a Cenozoic tempestite in the Qaidam Basin is significant in the paleogeographic, paleoclimate and paleostructural fields, which provides a new insight in further study of the Qinghai-Tibet Plateau uplift. [ABSTRACT FROM AUTHOR]

[Display omitted] • Reflux seepage, burial and hydrothermal types of dolomite in the Cambrian Sanshanzi Formation are petrographically and geochemically identified. • Reflux seepage dolomitization was formed by high-salinity and Mg2+-enriched fluid penetrates downward into the limestone, and the dolomite has low δ 13C, high Sr and low Mn contents. • Burial dolomitization was due to the limestone deeply buried during the diagenetic stage and formed under a high-temperature and pressure environment. • Hydrothermal dolomitization occurred during Mg2+-rich hydrothermal fluid invaded, and the dolomite characterized by saddle dolomite with a positive δ Eu anomaly, and a low δ 18O value. The Cambrian Sanshanzi Formation is an important dolomite horizon in the Ordos Basin of northern China, and is well exposed in the western part of that basin. This paper focuses on the petrography and geochemistry of dolomites in this formation with an aim to provide a better understanding of their genesis. Reflux seepage, burial, and hydrothermal dolomites are identified in the Sa nshanzi Formation. Reflux seepage dolomites include dolomitic grainstone and powder crystal dolomite, and have high Sr and low Mn contents, a high CaO/MgO ratio and low δ 13 C values, and the reflux seepage dolomitization was formed by high-salinity and Mg2+-enriched fluid penetrates downward into the limestone. Burial dolomites are the main type of dolomite distributed through the Sanshanzi Formation. Burial dolomites are composed of fine- to coarse-crystal dolomite and have low Sr and high Mn contents, a low CaO/MgO ratio, and high δ 13C values. The features of high salinity, strong reducibility and negative δ 18O values indicate the burial dolomites formed under high-temperature and high-pressure conditions, the burial dolomitization was due to the limestone deeply buried during the later diagenetic stage. Hydrothermal dolomites are mainly characterized by saddle dolomite features, a positive δ Eu anomaly, and low δ 18O values, and the hydrothermal dolomitization occurred during Mg2+-rich hydrothermal fluid invaded. The reflux seepage and hydrothermal dolomite developed in local areas, with the hydrothermal dolomite affected by the distribution of faults. [ABSTRACT FROM AUTHOR]

This paper deals with an initial-boundary problem of the fourth-order parabolic equation involving two logarithm terms. First, we give some results for blow-up or global solutions through classifying the initial energy and the Nehari energy. Second, we show asymptotic estimates about blow-up time and a large time estimate of solutions, respectively. [ABSTRACT FROM AUTHOR]

In this article, we consider non-negative solutions of the homogeneous Dirichlet problems of parabolic equations with local or nonlocal nonlinearities, involving variable exponents. We firstly obtain the necessary and sufficient conditions on the existence of blow-up solutions, and also obtain some Fujita-type conditions in bounded domains. Secondly, the blow-up rates are determined, which are described completely by the maximums of the variable exponents. Thirdly, we show that the blow-up occurs only at a single point for the equations with local nonlinearities, and in the whole domain for nonlocal nonlinearities. [ABSTRACT FROM PUBLISHER]

Abstract: This paper cares about blowup solutions for a system of n-componential heat equations coupled via localized reactions and with variable exponents. The criteria for non-simultaneous and simultaneous blowup are established for radial solutions with or without assumptions on initial data, including the existence of non-simultaneous blowup for n components; any blowup must be simultaneous or non-simultaneous. [Copyright &y& Elsevier]

Abstract: This paper considers blow-up solutions for reaction–diffusion equations, complemented by homogeneous Dirichlet boundary conditions. It is proved that there exist initial data such that one block or two (separated or contiguous) blocks of components blow up simultaneously while the others remain bounded. As a corollary, a necessary and sufficient condition is obtained such that any blow-up must be the case for at least two components blowing up simultaneously. We also show some other exponent regions, where any blow-up of components must be simultaneous. Moreover, the corresponding blow-up rates and sets are discussed. The results extend those in Liu and Li [B.C. Liu, F.J. Li, Non-simultaneous blow-up of components for nonlinear parabolic systems, J. Math. Anal. Appl. 356 (2009) 215–231]. [Copyright &y& Elsevier]

Abstract: This paper deals with u t =Δu + u m (x, t)e pv(0,t), v t =Δv + u q (0, t)e nv(x,t), subject to homogeneous Dirichlet boundary conditions. The complete classification on non-simultaneous and simultaneous blow-up is obtained by four sufficient and necessary conditions. It is interesting that, in some exponent region, large initial data u 0(v 0) leads to the blow-up of u(v), and in some betweenness, simultaneous blow-up occurs. For all of the nonnegative exponents, we find that u(v) blows up only at a single point if m >1(n >0), while u(v) blows up everywhere for 0⩽ m ⩽1 (n =0). Moreover, blow-up rates are considered for both non-simultaneous and simultaneous blow-up solutions. [Copyright &y& Elsevier]

Abstract: This work deals with non-simultaneous and simultaneous blow-up solutions for , , subject to homogeneous Dirichlet boundary conditions. We obtain the complete results of non-simultaneous and simultaneous blow-up solutions for any fixed point in any general bounded domain. The critical exponents of non-simultaneous blow-up are proposed. [Copyright &y& Elsevier]

Abstract: This paper deals with blow-up solutions in parabolic equations coupled via nonlocal nonlinearities, subject to homogeneous Dirichlet conditions. Firstly, some criteria on non-simultaneous and simultaneous blow-up are given, including four kinds of phenomena: (i) the existence of non-simultaneous blow-up; (ii) the coexistence of non-simultaneous and simultaneous blow-up; (iii) any blow-up must be simultaneous; (iv) any blow-up must be non-simultaneous. Next, total versus single point blow-up are classified completely. Moreover, blow-up rates are obtained for both non-simultaneous and simultaneous blow-up solutions. [Copyright &y& Elsevier]

Abstract: This paper deals with localized parabolic equations , with homogeneous Dirichlet boundary conditions, where is any fixed point in a bounded domain of . The optimal classification of non-simultaneous and simultaneous blow-up phenomena is proposed for all of the nonnegative exponents. Moreover, uniform blow-up profiles are obtained for all kinds of simultaneous blow-up solutions. [Copyright &y& Elsevier]

Abstract: This paper deals with the non-simultaneous and simultaneous blow-up for some parabolic systems coupled via nonlinear boundary flux . For radially symmetric solutions, we obtain that one component can blow up by itself and may provide sufficient help to the blow-up of the other ones under suitable initial data. In particular, such phenomena happen for every initial data in some exponent regions. It is interesting that there exist initial data such that any two components blow up simultaneously, either of which blows up depending on itself and also can give sufficient help to the other components blowing up simultaneously. A necessary and sufficient condition is obtained on the simultaneous blow-up of at least two components for all initial data. Moreover, the non-simultaneous and simultaneous blow-up rates and sets are determined. [Copyright &y& Elsevier]

Abstract: The critical exponents are established for a nonlinear diffusion system with convection, which are described clearly by the signs of two parameters solving the so-called characteristic algebraic system. It is proved that the convection plays an important role in determining the critical properties of solutions in the balance case. This greatly improves the authors’ previous paper for the same model. [Copyright &y& Elsevier]

Abstract: This paper deals with simultaneous and non-simultaneous blow-up solutions for heat equations coupled via exponential sources, subject to null Dirichlet boundary conditions. The main results complete the previously known results on the optimal classification for simultaneous and non-simultaneous blow-up solutions by covering the whole ranges of exponents. Moreover, all kinds of simultaneous and non-simultaneous blow-up rates are obtained. [Copyright &y& Elsevier]

Abstract: This paper deals with non-simultaneous and simultaneous blow-up for radially symmetric solution to heat equations coupled via nonlinear boundary . It is proved that there exist suitable initial data such that blows up alone if and only if . All of the classifications on the existence of only two components blowing up simultaneously are obtained. We find that different positions (different values of k, i, n) of and leads to quite different blow-up rates. It is interesting that different initial data lead to different blow-up phenomena even with the same requirements on exponent parameters. We also propose that blow up simultaneously while the other ones remain bounded in different exponent regions. Moreover, the blow-up rates and blow-up sets are obtained. [Copyright &y& Elsevier]

Abstract: The paper deals with the radially symmetric solutions of , , subject to null Dirichlet boundary conditions. For the blow-up classical solutions, we propose the critical exponents for non-simultaneous blow-up by determining the complete and optimal classification for all the non-negative exponents: (i) There exist initial data such that () blows up alone if and only if (), which means that any blow-up is simultaneous if and only if , . (ii) Any blow-up is () blowing up with () remaining bounded if and only if , (, ). (iii) Both non-simultaneous and simultaneous blow-up may occur if and only if , . Moreover, we consider the blow-up rate and set estimates which were not obtained in the previously known work for the same model. [Copyright &y& Elsevier]