Tree maps having chain movable fixed points

In this paper we discuss some basic properties of chain reachable sets and chain equivalent sets of continuous maps. It is proved that if f:T→T is a tree map which has a chain movable fixed point v, and the chain equivalent set CE(v,f) is not contained in the set P(f) of periodic points of f, then there exists a positive integer p not greater than the number of points in the set End([CE(v,f)])−Pv(f) such that fp is turbulent, and the topological entropy . This result generalizes the corresponding results given in Block and Coven (1986) [2], Guo et al. (2003) [6], Sun and Liu (2003) [10], Ye (2000) [11], Zhang and Zeng (2004) [12]. In addition, in this paper we also consider metric spaces which may not be trees but have open subsets U such that the closures are trees. Maps of such metric spaces which have chain movable fixed points are discussed.     

Existence and convergence of solutions of singular boundary value problems for second order ordinary differential equations and applications

In this paper,we consider the singular boundary value problems for second order quasilinear ordinary differential equations and prove existence and convergence on second order perturbation terms.The result is applied to solve the Riemann problem for 2×2 hyperbolic conservation laws,which is a partial differential equation arising in applied mathematical area.     

Loewy Modules with Finite Loewy Invariants and Max Modules with Finite Radical Invariants

Over a commutative ring R, a module is artinian if and only if it is a Loewy module with finite Loewy invariants [5 Facchini , A. ( 1981 ). Loewy and artinian modules over commutative rings . Ann. Mat. Pura Appl. 128 : 359 – 374 .[Crossref], [Web of Science ®] , [Google Scholar]]. In this paper, we show that this is not necesarily true for modules over noncommutative rings R, though every artinian module is always a Loewy module with finite Loewy invariants. We prove that every Loewy module with finite Loewy invariants has a semilocal endomorphism ring, thus generalizing a result proved by Camps and Dicks for artinian modules [3 Camps , R. , Dicks , W. ( 1993 ). On semilocal rings . Israel J. Math. 81 : 203 – 211 .[Crossref], [Web of Science ®] , [Google Scholar]]. Finally, we obtain similar results for the dual class of max modules.     

A Convenient Synthetic Route of Diethyl (4‐Oxo‐chromeno[2,3‐d]pyrimidin‐2(5)‐yl)phosphonates

Novel diethyl (4‐oxo‐3,4‐dihydro‐2H‐chromeno[2,3‐d]pyrimidin‐2‐yl)phosphonate as two enantiomers and diethyl (4‐oxo‐1,5‐dihydro‐4H‐chromeno[2,3‐d]pyrimidin‐5‐yl) phosphonate were obtained in easy procedure via reaction of 2‐imino‐2H‐chromene‐3‐carboxamide, dimethylformamide dimethyl‐acetal, and diethyl phosphite in a simple one pot. Possible reaction mechanisms were proposed. The structures of the obtained products were confirmed by elemental analyses and spectral tools.     

Size‐dependent Tumor Response to Photodynamic Therapy and Irinotecan Monotherapies Revealed by Longitudinal Ultrasound Monitoring in an Orthotopic Pancreatic Cancer Model

Longitudinal monitoring of tumor size in vivo can provide important biological information about disease progression and treatment efficacy that is not captured by other modes of quantification. Ultrasound enables high‐throughput evaluation of orthotopic mouse models via fast acquisition of three‐dimensional tumor images and calculation of volume with a reasonable degree of accuracy. Herein, we compare orthotopic pancreatic tumor volume measurements determined by ultrasound with volume measured by calipers and tumor weight, and found strong correlations between the three modalities over a large range of tumor sizes, suggesting ultrasound can accurately quantify tumor volumes in this model. Furthermore, we demonstrate the unique ability of longitudinal treatment monitoring to reveal a tumor size‐dependent response to Benzoporphyrin Derivative photodynamic therapy (BPD‐PDT) and irinotecan. Small tumors (5–35 mm³) were found to respond well to a single round of PDT, while large tumors (35–65 mm³) showed no response to the same treatment. These results highlight the role that tumor size can play in preclinical interpretation of treatment response and more generally suggest that careful evaluation of subtle biological features such as this must be carefully considered in order to grant a more comprehensive understanding of disease biology in vivo.     

A Robust Solid Electrolyte Interphase Layer Augments the Ion Storage Capacity of Bimetallic‐Sulfide‐Containing Potassium‐Ion Batteries

Metal–organic framework‐derived NiCo_2.5S₄ microrods wrapped in reduced graphene oxide (NCS@RGO) were synthesized for potassium‐ion storage. Upon coordination with organic potassium salts, NCS@RGO exhibits an ultrahigh initial reversible specific capacity (602 mAh g^?1 at 50 mA g^?1) and ultralong cycle life (a reversible specific capacity of 495 mAh g^?1 at 200 mA g^?1 after 1 900 cycles over 314 days). Furthermore, the battery demonstrates a high initial Coulombic efficiency of 78 %, outperforming most sulfides reported previously. Advanced ex situ characterization techniques, including atomic force microscopy, were used for evaluation and the results indicate that the organic potassium salt‐containing electrolyte helps to form thin and robust solid electrolyte interphase layers, which reduce the formation of byproducts during the potassiation–depotassiation process and enhance the mechanical stability of electrodes. The excellent conductivity of the RGO in the composites, and the robust interface between the electrodes and electrolytes, imbue the electrode with useful properties; including, ultrafast potassium‐ion storage with a reversible specific capacity of 402 mAh g^?1 even at 2 A g^?1.     

Synthesis and Magnetic Characteristics of Neodymium Ferrite Powders with Perovskite Structure

Russian Journal of Applied Chemistry - Nanopowders of neodymium ferrite with perovskite structure were synthesized by co-precipitation precipitation via hydrolysis of iron(III) and neodymium(III)...     

A novel polypropylene composite filled by kaolin particles with β-nucleation

Kaolin-filled polypropylene (PP) composites generally form α-crystal due to the effect of kaolin with α-nucleation. The transition from α- to β-nucleation of kaolin has been investigated, and a novel kaolin with β-nucleation (β-kaolin) and kaolin-filled PP composites with high β-crystal content were prepared first. The DSC and WAXD results indicated that the β-kaolin exhibits stronger β-nucleating ability than CaPA as β-nucleating agent for PP crystallization. It is found that the β-crystal content has been influenced little by filler contents in β-kaolin-filled PP composites. Mechanical properties and spherulitic morphology of filled PP composites was characterized. The synergistic effect of filler and β-crystal significantly improved impact strength of kaolin-filled PP composites.

     

Up-regulation of Na expression in the area postrema of total sleep deprived rats by TOF-SIMS analysis

Area postrema (AP) is a circumventricular organ plays an important role in sodium homeostasis and cardiovascular regulation. Since sleep deficiency will cause cardiovascular dysfunction, the present study aims to determine whether sodium level would significantly alter in AP following total sleep deprivation (TSD). Sodium level was investigated in vivo by time-of-flight secondary ion mass spectrometry (TOF-SIMS). Clinical manifestation of cardiovascular function was demonstrated by mean arterial pressure (MAP) values. Results indicated that in normal rats, TOF-SIMS spectrum revealed a major peak of sodium ion counting as 5.61 × 10⁵ at m/z 23. The sodium ions were homogeneous distributed in AP without specific localization. However, following TSD, the sodium intensity was relatively increased (6.73 × 10⁵) and the signal for sodium image was strongly expressed throughout AP with definite spatial distribution. MAP of TSD rats is 138 ± 5 mmHg, which is significantly higher than that of normal ones (121 ± 3 mmHg). Regarding AP is an important area for sodium sensation and development of hypernatremic related sympatho-excitation; up-regulation of sodium expression following TSD suggests that high sodium level might over-activate AP, through complex neuronal networks involving in sympathetic regulation, which could lead to the formation of TSD relevant cardiovascular diseases.