Continuity of truncated Hardy-Littlewood maximal function

This paper focuses on the continuity of the truncated Hardy-Littlewood maximal function.We first show that the truncated Hardy-Littlewood maximal function is lower semi-continuous.Then by investigating the behavior of the truncated Hardy-Littlewood maximal function when the truncated parameterγchanges,we obtain an equivalent condition of the continuity of the truncated Hardy-Littlewood maximal function.

Analytical Solution and Simplified Formula for Added Mass of Horizontal and Vertical Motions of Truncated Cylinders Under Earthquake Action

This paper investigates the hydrodynamic characteristics of floating truncated cylinders undergoing horizontal and vertical motions due to earthquake excitations in the finite water depth.The governing equation of the hydrodynamic pressure acting on the cylinder is derived based on the radiation theory with the inviscid and incompressible assumptions.The governing equation is solved by using the method of separating variables and analytical solutions are obtained by assigning reasonable boundary conditions.The analytical result is validated by a numerical model using the exact artificial boundary simulation of the infinite water.The main variation and distribution characteristics of the hydrodynamic pressure acting on the side and bottom of the cylinder are analyzed for different combinations of wide-height and immersion ratios.The added mass coefficient of the cylinder is calculated by integrating the hydrodynamic pressure and simplified formulas are proposed for engineering applications.The calculation results show that the simplified formulas are in good agreement with the analytical solutions.

CRISPR/Cas9-mediated NlInR2 mutants:Analyses of residual mRNA and truncated proteins

CRISPR/Cas9 technology is a powerful genome manipulation tool in insects.However,little is known about whether mRNA and protein of a target gene are completely cleared in homozygous mutants.This study generated homozygous mutants of the insulin receptor gene 2(NlInR2)in the brown planthopper(Nilaparvata lugens)using CRISPR/Cas9 genome editing.Both frameshift mutants,E5_D17 and E6_I7,differentiated towards long wings,but there were differences in wing morphology,with E5_D17 showing wing deformities.Subsequent investigations revealed the presence of residual expression of NlInR2 mRNA in both mutants,as well as the occurrence of spliceosomes featuring exon skipping splicing in E5_D17.Additionally,the E5_D17 exhibited the detection of N-terminally truncated NlInR2 protein.RNA interference experiments indicated that the knockdown of NlInR2 expression in the E5_D17 mutant line increased the proportion of wing deformities from 11.1 to 65.6%,suggesting that the residual NlInR2 mRNA of the E5_D17 mutant might have retained some genetic functions.Our results imply that systematic characterization of residual protein expression or function in CRISPR/Cas9-generated mutant lines is necessary for phenotypic interpretation.

Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

Quercetin inhibits truncated isoform of dopamine-and cAMP-regulated phosphoprotein as adjuvant treatment for trastuzumab therapy resistance in HER2-positive breast cancer

Trastuzumab resistance is one of the causes of poor prognosis in patients with human epidermal growth factor receptor 2(HER2)-positive(HER2+)breast cancer(BC).The truncated isoform of dopamine-and cAMPregulated phosphoprotein(t-DARPP)has been reported to be involved in trastuzumab therapy resistance and promoting tumor progression.To evaluate the t-DARPP expression in BC,paired tumors and surrounding normal tissues were analyzed by real-time polymerase chain reaction and confirmed higher DARPP-32 kDa family mRNA expression in HER2+BC tumor tissues.We established 2 patient-derived xenografts(PDX)mice models to test the efficacy of trastuzumab,named model 1(non-responder)and model 2(responder).t-DARPP and p95-HER2 protein-protein interactions were detected in PDX tumor tissue from non-responders using Förster resonance energy transfer assays.Instead,there is no response from the responder.Furthermore,mechanistic studies using transwell and western blot assays demonstrated that t-DARPP could upregulate epithelial-mesenchymal transition signaling proteins,enhance p95-HER2 expression and promote cell migration.We found that quercetin effectively reduced t-DARPP expression in HER2+BC cells.In t-DARPP ShRNA-suppressed cells,quercetin synergistically enhanced trastuzumab-induced apoptotic cell death and G2/M phase arrest.In conclusion,the combination of quercetin and trastuzumab treatment by targeting t-DARPP in HER2+BC patients has the potential as a biomarker for mitigating drug resistance.

Explicit Isogeometric Topology Optimization Method with Suitably Graded Truncated Hierarchical B-Spline

This work puts forward an explicit isogeometric topology optimization(ITO)method using moving morphable components(MMC),which takes the suitably graded truncated hierarchical B-Spline based isogeometric analysis as the solver of physical unknown(SGTHB-ITO-MMC).By applying properly basis graded constraints to the hierarchical mesh of truncated hierarchical B-splines(THB),the convergence and robustness of the SGTHB-ITOMMC are simultaneously improved and the tiny holes occurred in optimized structure are eliminated,due to the improved accuracy around the explicit structural boundaries.Moreover,an efficient computational method is developed for the topological description functions(TDF)ofMMC under the admissible hierarchicalmesh,which consists of reducing the dimensionality strategy for design space and the locally computing strategy for hierarchical mesh.We apply the above SGTHB-ITO-MMC with improved efficiency to a series of 2D and 3Dcompliance design problems.The numerical results show that the proposed SGTHB-ITO-MMC method outperforms the traditional THB-ITO-MMCmethod in terms of convergence rate and efficiency.Therefore,the proposed SGTHB-ITO-MMC is an effective way of solving topology optimization(TO)problems.

Tau truncation in the pathogenesis of Alzheimer's disease:a narrative review

Alzheimer's disease is characterized by two major neuropathological hallmarks—the extracellularβ-amyloid plaques and intracellular neurofibrillary tangles consisting of aggregated and hyperphosphorylated Tau protein.Recent studies suggest that dysregulation of the microtubuleassociated protein Tau,especially specific proteolysis,could be a driving force for Alzheimer's disease neurodegeneration.Tau physiologically promotes the assembly and stabilization of microtubules,whereas specific truncated fragments are sufficient to induce abnormal hyperphosphorylation and aggregate into toxic oligomers,resulting in them gaining prion-like characteristics.In addition,Tau truncations cause extensive impairments to neural and glial cell functions and animal cognition and behavior in a fragment-dependent manner.This review summarizes over 60 proteolytic cleavage sites and their corresponding truncated fragments,investigates the role of specific truncations in physiological and pathological states of Alzheimer's disease,and summarizes the latest applications of strategies targeting Tau fragments in the diagnosis and treatment of Alzheimer's disease.

Evolutionary Plasmonic Properties of Single Truncated Ag Nanowire-on-Au Film Nanocavity

Noble metal nanocavities have been widely demonstrated to possess great potential applications in nanooptics and nanophotonics due to their extraordinary localized surface plasmon resonance.However,most metal nanocrystals synthesized by chemical methods often suffer from truncation with different degrees due to oxidation and dissolution of metal atoms at corner and edges.We investigate the influence of shape truncation on the plasmonic properties of single Ag nanowire on Au film nanocavity using the finite difference time domain method.When the Ag nanowire(the circumradius R_(2)=50 nm)is gradually truncated from pentagonal to circular geometry,the scattering peak position of the nanocavity shows prominent blue shift from 962 nm to 608 nm,suggesting a nonnegligible role of truncation on plasmonic properties.The electric field strength and charge distribution of the structure reveal the evolution from dipole mode to quadrupole mode.It is also found that the plasmon resonance wavelength is linearly dependent on the truncation ratio R_(1)/R_(2)(R_(1) is the inradius)and the modulation slope is also reliable to the size of Ag nanowire.Our observations could shed light on developing high-performance tunable optical nano-devices in future.

The Doubly Truncated Generalized Log-Lindley Distribution

The aim of this paper is to present generalized log-Lindely (GLL) distribution, as a new model, and find doubly truncated generalized log-Lindely (DTGLL) distribution, truncation in probability distributions may occur in many studies such as life testing, and reliability. We illustrate the applicability of GLL and DTGLL distributions by Real data application. The GLL distribution can handle the risk rate functions in the form of panich and increase. This property makes GLL useful in survival analysis. Various statistical and reliability measures are obtained for the model, including hazard rate function, moments, moment generating function, mean and variance, quantiles function, Skewness and kurtosis, mean deviations, mean inactivity time and strong mean inactivity time. The estimation of model parameters is justified by the maximum Likelihood method. An application to real data shows that DTGLL distribution can provide better suitability than GLL and some other known distributions.

Different wave patterns for two-coupled Maccari's system with complex structure via truncated Painlevéapproach

We focused on the two-coupled Maccari's system.With the help of truncated Painlevéapproach(TPA),we express local solution in the form of arbitrary functions.From the solution obtained,using its appropriate arbitrary functions,we have generated the rogue wave pattern solutions,rogue wave solutions,and lump solutions.In addition,by controlling the values of the parameters in the solutions,we show the dynamic behaviors of the rogue wave pattern solutions,rogue wave solutions,and lump solutions with the aid of Maple tool.The results of this study will contribute to the understanding of nonlinear wave dynamics in higher dimensional Maccari's systems.

Numerical simulation of a truncated cladding negative curvature fiber sensor based on the surface plasmon resonance effect

A refractive index(RI)sensor based on the surface plasmon resonance effect is proposed using a truncated cladding negative curvature fiber(TC-NCF).The influences of the TC-NCF structure parameters on the sensing performances are investigated and compared with the traditional NCF.The simulation results show that the proposed TC-NCF RI sensor has an ultra-wide detection range from 1.16 to 1.43.The maximum wavelength sensitivity reaches 12400 nm/RIU,and the corresponding R^(2)of the polynomial fitting equation is 0.9999.The maximum and minimum resolutions are 2.56×10^(-5)and 8.06×10^(-6),respectively.In addition,the maximum amplitude sensitivity can reach-379.1 RIU^(-1)when the RI is chosen as 1.43.The proposed TC-NCF RI sensor could be useful in biochemical medicine,environmental monitoring,and food safety.

Pricing European Options Based on a Logarithmic Truncated t-Distribution

The t-distribution has a “fat tail” feature, which is more suitable than the normal probability density function to describe the distribution characteristics of return on assets. The difficulty of using t-distribution to price European options is that a fat tail can lead to a deviation in one integral required for option pricing. We use a distribution called logarithmic truncated t-distribution to price European options. A risk neutral valuation method was used to obtain a European option pricing model with logarithmic truncated t-distribution.

Pro-resolving lipid mediator reduces amyloid-β42–induced gene expression in human monocyte–derived microglia

Specialized pro-resolving lipid mediators including maresin 1 mediate resolution but the levels of these are reduced in Alzheimer's disease brain, suggesting that they constitute a novel target for the treatment of Alzheimer's disease to prevent/stop inflammation and combat disease pathology. Therefore, it is important to clarify whether they counteract the expression of genes and proteins induced by amyloid-β. With this objective, we analyzed the relevance of human monocyte–derived microglia for in vitro modeling of neuroinflammation and its resolution in the context of Alzheimer's disease and investigated the pro-resolving bioactivity of maresin 1 on amyloid-β42–induced Alzheimer's disease–like inflammation. Analysis of RNA-sequencing data and secreted proteins in supernatants from the monocyte-derived microglia showed that the monocyte-derived microglia resembled Alzheimer's disease–like neuroinflammation in human brain microglia after incubation with amyloid-β42. Maresin 1 restored homeostasis by down-regulating inflammatory pathway related gene expression induced by amyloid-β42 in monocyte-derived microglia, protection of maresin 1 against the effects of amyloid-β42 is mediated by a re-balancing of inflammatory transcriptional networks in which modulation of gene transcription in the nuclear factor-kappa B pathway plays a major part. We pinpointed molecular targets that are associated with both neuroinflammation in Alzheimer's disease and therapeutic targets by maresin 1. In conclusion, monocyte-derived microglia represent a relevant in vitro microglial model for studies on Alzheimer's disease-like inflammation and drug response for individual patients. Maresin 1 ameliorates amyloid-β42–induced changes in several genes of importance in Alzheimer's disease, highlighting its potential as a therapeutic target for Alzheimer's disease.

Jiaohong pills attenuate neuroinflammation and amyloid-βprotein-induced cognitive deficits by modulating the mitogen-activated protein kinase/nuclear factor kappa-B pathway

Background:Jiaohong pills(JHP)consist of Pericarpium Zanthoxyli(PZ)and Radix Rehmanniae,two herbs that have been extensively investigated over many years due to their potential protective effects against cognitive decline and memory impairment.However,the precise mechanisms underlying the beneficial effects remain elusive.Here,research studies were conducted to investigate and validate the therapeutic effects of JHP on Alzheimer's disease.Methods:BV-2 cell inflammation was induced by lipopolysaccharide.AD mice were administered amyloid-β(Aβ).Behavioral experiments were used to evaluate learning and memory ability.The levels of nitric oxide(NO),tumor necrosis factor-alpha(TNF-α),interleukin-1β(IL-1β),and interleukin-10(IL-10)were detected using enzymelinked immunosorbent assay(ELISA).The protein expressions of inducible nitric oxide synthase(iNOS)and the phosphorylation level of mitogen-activated protein kinase(MAPK)and nuclear factor kappa-B(NF-κB)were detected using Western blot.Nissl staining was used to detect neuronal degeneration.Results:The results demonstrated that an alcoholic extract of PZ significantly decreased the levels of NO,IL-1β,TNF-α,and iNOS;increased the expression level of IL-10;and significantly decreased the phosphorylation levels of MAPK and NF-κB.These inhibitory effects were further confirmed in the AD mouse model.Meanwhile,JHP improved learning and memory function in AD mice,reduced neuronal damage,and enriched the Nissl bodies in the hippocampus.Moreover,IL-1βand TNF-αin the cortex were significantly downregulated after JHP administration,whereas IL-10showed increased expression.Conclusions:It was found that JHP reduced neuroinflammatory response in AD mice by targeting the MAPK/NF-κB signaling pathway.

FUBP3 mediates the amyloid-β-induced neuronal NLRP3 expression

Alzheimer's disease is characterized by deposition of amyloid-β,which forms extracellular neuritic plaques,and accumulation of hyperphosphorylated tau,which aggregates to form intraneuronal neurofibrillary tangles,in the brain.The NLRP3 inflammasome may play a role in the transition from amyloid-βdeposition to tau phosphorylation and aggregation.Because NLRP3 is primarily found in brain microglia,and tau is predominantly located in neurons,it has been suggested that NLRP3 expressed by microglia indirectly triggers tau phosphorylation by upregulating the expression of pro-inflammatory cytokines.Here,we found that neurons also express NLRP3 in vitro and in vivo,and that neuronal NLRP3 regulates tau phosphorylation.Using biochemical methods,we mapped the minimal NLRP3 promoter and identified FUBP3 as a transcription factor regulating NLRP3 expression in neurons.In primary neurons and the neuroblastoma cell line Neuro2A,FUBP3 is required for endogenous NLRP3 expression and tau phosphorylation only when amyloid-βis present.In the brains of aged wild-type mice and a mouse model of Alzheimer's disease,FUBP3 expression was markedly increased in cortical neurons.Transcriptome analysis suggested that FUBP3 plays a role in neuron-mediated immune responses.We also found that FUBP3 trimmed the 5′end of DNA fragments that it bound,implying that FUBP3 functions in stress-induced responses.These findings suggest that neuronal NLRP3 may be more directly involved in the amyloid-β-to–phospho-tau transition than microglial NLRP3,and that amyloid-βfundamentally alters the regulatory mechanism of NLRP3 expression in neurons.Given that FUBP3 was only expressed at low levels in young wild-type mice and was strongly upregulated in the brains of aged mice and Alzheimer's disease mice,FUBP3 could be a safe therapeutic target for preventing Alzheimer's disease progression.

Enhanced autophagic clearance of amyloid-βvia histone deacetylase 6-mediated V-ATPase assembly and lysosomal acidification protects against Alzheimer's disease in vitro and in vivo

Recent studies have suggested that abnormal acidification of lysosomes induces autophagic accumulation of amyloid-βin neurons,which is a key step in senile plaque formation.Therefore,resto ring normal lysosomal function and rebalancing lysosomal acidification in neurons in the brain may be a new treatment strategy for Alzheimer's disease.Microtubule acetylation/deacetylation plays a central role in lysosomal acidification.Here,we show that inhibiting the classic microtubule deacetylase histone deacetylase 6 with an histone deacetylase 6 shRNA or thehistone deacetylase 6 inhibitor valproic acid promoted lysosomal reacidification by modulating V-ATPase assembly in Alzheimer's disease.Fu rthermore,we found that treatment with valproic acid markedly enhanced autophagy.promoted clearance of amyloid-βaggregates,and ameliorated cognitive deficits in a mouse model of Alzheimer's disease.Our findings demonstrate a previously unknown neuroprotective mechanism in Alzheimer's disease,in which histone deacetylase 6 inhibition by valproic acid increases V-ATPase assembly and lysosomal acidification.

A truncated implicit high-order finite-difference scheme combined with boundary conditions

In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.

Acquisition of Insect-Resistant Transgenic Maize Harboring a Truncated cry1Ah Gene via Agrobacterium-Mediated Transformation

A novel insecticidal gene crylAh was cloned from Bacillus thuringiensis isolate BT8 previously for plant genetic engineering improvement. Truncated active CrylAh toxin has a toxicity level similar to that of the full-length CrylAh toxin. In this study, plant expression vector pMhGM harboring truncated crylAh gene was transformed into maize （Zea mays L.） immature embryos by Agrobacterium tumefaciens-mediated transformation at which maize alcohol dehydrogenase matrix attachment regions （madMARs） were incorporated on both sides of the gene expression cassette to improve gene expression. A total of 23 PCR positive events were obtained with a transformation efficiency of 5% around. Bioassay results showed that events 1-4 and 1-5 exhibited enhanced resistance to the Asian corn borer （Ostriniafurnacalis）. These two events were further confirmed by molecular analysis. Southern blot suggested that a single copy of the crylAh gene was successfully integrated into the maize genome. Western blot and ELISA showed that the foreign gene crylAh was expressed stably at high level in maize and could be inherited stably over generations. The results of a bioassay of T l-T4 transgenic maize plants indicated that the transgenic plants were highly toxic to the Asian corn borer and their resistance could be inherited stably from generation to generation. Thus, events 1-4 and 1-5 are good candidates for the breeding of insect-resistant maize.

Numerical modeling of wave equation by a truncated high-order finite-difference method

Finite-difference methods with high-order accuracy have been utilized to improve the precision of numerical solution for partial differential equations. However, the computation cost generally increases linearly with increased order of accuracy. Upon examination of the finite-difference formulas for the first-order and second-order derivatives, and the staggered finite-difference formulas for the first-order derivative, we examine the variation of finite-difference coefficients with accuracy order and note that there exist some very small coefficients. With the order increasing, the number of these small coefficients increases, however, the values decrease sharply. An error analysis demonstrates that omitting these small coefficients not only maintain approximately the same level of accuracy of finite difference but also reduce computational cost significantly. Moreover, it is easier to truncate for the high-order finite-difference formulas than for the pseudospectral for- mulas. Thus this study proposes a truncated high-order finite-difference method, and then demonstrates the efficiency and applicability of the method with some numerical examples.

UNIQUENESS PROBLEM FOR MEROMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES INTO P^N(C) WITH TRUNCATED MULTIPLICITIES

This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space p^N（C） with truncated multiplicities, and our results improve some earlier work.