BOUND STATES FOR A STATIONARY NONLINEAR SCHRDINGER-POISSON SYSTEM WITH SIGN-CHANGING POTENTIAL IN R^3

We study the following Schrodinger-Poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 ＋∞, V（x） and Q（x）=1 ,D.Ruiz[19] proved that（Pλ）with p∈ （2, 5） has always a positive radial solution, but （Pλ） with p E （1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that（Pλ）with p ∈（1＋∞）has alaways a bound state（H^1（R^3）solution for λ∈[0,λ0）and certain functions V（x）and Q（x）in L^∞（R^3）.Moreover,for every λ∈[0,λ0）,the solutions uλ of （Pλ）converges,along a subsequence,to a solution of （P0）in H^1 as λ→0

MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRDINGER-POISSON EQUATIONS WITH SIGN-CHANGING POTENTIAL

In this article, we study the following nonhomogeneous Schrodinger-Poissone quations{-△u＋λV（x）u＋K（x）Фu=f（x,u）＋g（x）,x∈R^3,-△Ф=k（x）u^2, x∈R^3}where λ 〉 0 is a parameter. Under some suitable assumptions on 11, K, f and g, the existence of multiple solutions is proved by using the Ekeland＇s variational principle and the Mountain Pass Theorem in critical point theory. In particular, the potential V is allowed to be signchanging.

SIGN-CHANGING SOLUTIONS FOR SCHRDINGER EQUATIONS WITH VANISHING AND SIGN-CHANGING POTENTIALS

In this article, we study the existence of sign-changing solutions for the following SchrSdinger equation -△u ＋ λV（x）u = K（x）｜u｜^p-2u x∈R^N, u→0 as ｜x｜→ ＋∞, 2N where N ≥ 3, λ〉 0 is a parameter, 2 〈 p 〈 2N/N-2, and the potentials V（x） and K（x） satisfy some suitable conditions. By using the method based on invariant sets of the descending flow, we obtain the existence of a positive ground state solution and a ground state sign-changing solution of the above equation for small λ, which is a complement of the results obtained by Wang and Zhou in [J. Math. Phys. 52, 113704, 2011].

THE EXISTENCE AND CONCENTRATION OF GROUND STATE SIGN-CHANGING SOLUTIONS FOR KIRCHHOFF-TYPE EQUATIONS WITH A STEEP POTENTIAL WELL

In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a steep potential well and the nonlinearity f∈C(R,R)satisfies certain assumptions.By applying a signchanging Nehari manifold combined with the method of constructing a sign-changing(PS)C sequence,we obtain the existence of ground state sign-changing solutions with precisely two nodal domains when λ is large enough,and find that its energy is strictly larger than twice that of the ground state solutions.In addition,we also prove the concentration of ground state sign-changing solutions.

Quantitative effect of kerogen type on the hydrocarbon generation potential of Paleogene lacustrine source rocks,Liaohe Western Depression,China

Kerogen types exert a decisive effect on the onset and capacity of hydrocarbon generation of source rocks.Lacustrine source rocks in the Liaohe Western Depression are characterized by thick deposition,high total organic carbon(TOC)content,various kerogen types,and a wide range of thermal maturity.Consequently,their hydrocarbon generation potential and resource estimation can be misinterpreted.In this study,geochemical tests,numerical analysis,hydrocarbon generation kinetics,and basin modeling were integrated to investigate the differential effects of kerogen types on the hydrocarbon generation potential of lacustrine source rocks.Optimized hydrocarbon generation and expulsion(HGE)models of different kerogen types were established quantitatively upon abundant Rock-Eval/TOC/vitrinite reflectance(R_(o))datasets.Three sets of good-excellent source rocks deposited in the fourth(Es4),third(Es3),and first(Es1)members of Paleogene Shahejie Formation,are predominantly types I-II_(1),II_(1)-II_(2),and II-III,respectively.The activation energy of types I-II_(2)kerogen is concentrated(180-230 kcal/mol),whereas that of type III kerogen is widely distributed(150-280 kcal/mol).The original hydrocarbon generation potentials of types I,II_(1),II_(2),and III kerogens are 790,510,270,and 85 mg/g TOC,respectively.The Ro values of the hydrocarbon generation threshold for type I-III source rocks gradually increase from 0.42%to 0.74%,and Ro values of the hydrocarbon expulsion threshold increase from 0.49%to 0.87%.Types I and II_(1)source rocks are characterized by earlier hydrocarbon generation,more rapid hydrocarbon expulsion,and narrower hydrocarbon generation windows than types II_(2)and III source rocks.The kerogen types also affect the HGE history and resource potential.Three types(conventional,tight,and shale oil/gas)and three levels(realistic,expected,and prospective)of hydrocarbon resources of different members in the Liaohe Western Depression are evaluated.Findings suggest that the Es3 member has considerable conventional and unconventional hydrocarbon resources.This study can quantitatively characterize the hydrocarbon generation potential of source rocks with different kerogen types,and facilitate a quick and accurate assessment of hydrocarbon resources,providing strategies for future oil and gas exploration.

Transient receptor potential channels as predictive marker and potential indicator of chemoresistance in colon cancer

Transient receptor potential(TRP)channels are strongly associated with colon cancer development and progression.This study leveraged a multivariate Cox regression model on publicly available datasets to construct a TRP channels-associated gene signature,with further validation of signature in real world samples from our hospital treated patient samples.Kaplan-Meier(K-M)survival analysis and receiver operating characteristic(ROC)curves were employed to evaluate this gene signature’s predictive accuracy and robustness in both training and testing cohorts,respectively.Additionally,the study utilized the CIBERSORT algorithm and single-sample gene set enrichment analysis to explore the signature’s immune infiltration landscape and underlying functional implications.The support vector machine algorithm was applied to evaluate the signature’s potential in predicting chemotherapy outcomes.The findings unveiled a novel three TRP channels-related gene signature(MCOLN1,TRPM5,and TRPV4)in colon adenocarcinoma(COAD).The ROC and K-M survival curves in the training dataset(AUC=0.761;p=1.58e-05)and testing dataset(AUC=0.699;p=0.004)showed the signature’s robust predictive capability for the overall survival of COAD patients.Analysis of the immune infiltration landscape associated with the signature revealed higher immune infiltration,especially an increased presence of M2 macrophages,in high-risk group patients compared to their low-risk counterparts.High-risk score patients also exhibited potential responsiveness to immune checkpoint inhibitor therapy,evident through increased CD86 and PD-1 expression profiles.Moreover,the TRPM5 gene within the signature was highly expressed in the chemoresistance group(p=0.00095)and associated with poor prognosis(p=0.036)in COAD patients,highlighting its role as a hub gene of chemoresistance.Ultimately,this signature emerged as an independent prognosis factor for COAD patients(p=6.48e-06)and expression of model gene are validated by public data and real-world patients.Overall,this bioinformatics study provides valuable insights into the prognostic implications and potential chemotherapy resistance mechanisms associated with TRPs-related genes in colon cancer.

Geochemical fingerprints and hydrocarbon potential of Paleocene mudrocks in the Tano Basin, Ghana: insights from biomarkers and stable carbon isotopes

The Paleocene mudrocks in Ghana’s Tano Basin have received limited attention despite ongoing efforts to explore hydrocarbon resources.A thorough geochemical analysis is imperative to assess these mudrocks’petroleum generation potential and formulate effective exploration strategies.In this study,a comprehensive geochemical analysis was carried out on ten Paleocene rock cuttings extracted from TP-1,a discovery well within the Tano Basin.Various analytical techniques,including total organic carbon(TOC)analysis,Rock–Eval pyrolysis,gas chromatography-mass spectrometry,and isotope ratio-mass spectrometry,were employed to elucidate their hydrocar-bon potential and organic facies.Thefindings in this study were subsequently compared to existing geochemical data on Paleocene source rocks in the South Atlantic marginal basins.The results indicated that the Paleocene samples have TOC content ranging from 0.68 to 2.93 wt%.The prevalent kerogen types identified in these samples were Type Ⅱ and Type Ⅲ.Molecular and isotope data suggest that the organic matter found in the Paleocene mudrocks can be traced back to land plants and lower aquatic organisms.These mudrocks were deposited in a transi-tional environment withfluctuating water salinity,charac-terized by sub-oxic redox conditions.Maturity indices,both bulk and molecular,indicated a spectrum of maturity levels within the Paleocene mudrocks,spanning from immature to marginally mature,with increasing maturity observed with greater depth.In comparison,the organic composition and depositional environments of Paleocene source rocks in the Tano Basin closely resemble those found in the Niger Delta Basin,Douala,and Kribi-Campo Basins,the Kwanza Formation in Angola,and certain Brazilian marginal basins.However,it is worth noting that Paleocene source rocks in some of the basins,such as the Niger Delta and Brazilian marginal basins,exhibit rela-tively higher thermal maturity levels compared to those observed in the current Paleocene samples from the Tano Basin.In conclusion,the comprehensive geochemical analysis of Paleocene mudrocks within Ghana’s Tano Basin has unveiled their marginal hydrocarbon generation potential.The shared geochemical characteristics between the Paleocene mudrocks in the Tano Basin and those in the nearby South Atlantic marginal basins offer valuable insights into source rock quality,which is crucial for shaping future strategies in petroleum exploration in this region.

Natural gas exploration potential and favorable targets of Permian Fengcheng Formation in the western Central Depression of Junggar Basin,NW China

Based on the organic geochemical data and the molecular and stable carbon isotopic compositions of natural gas of the Lower Permian Fengcheng Formation in the western Central Depression of Junggar Basin,combined with sedimentary environment analysis and hydrocarbon-generating simulation,the gas-generating potential of the Fengcheng source rock is evaluated,the distribution of large-scale effective source kitchen is described,the genetic types of natural gas are clarified,and four types of favorable exploration targets are selected.The results show that:(1)The Fengcheng Formation is a set of oil-prone source rocks,and the retained liquid hydrocarbon is conducive to late cracking into gas,with characteristics of high gas-generating potential and late accumulation;(2)The maximum thickness of Fengcheng source rock reaches 900 m.The source rock has entered the main gas-generating stage in Penyijingxi and Shawan sags,and the area with gas-generating intensity greater than 20×10^(8) m^(3)/km^(2) is approximately 6500 km^(2).(3)Around the western Central Depression,highly mature oil-type gas with light carbon isotope composition was identified to be derived from the Fengcheng source rocks mainly,while the rest was coal-derived gas from the Carboniferous source rock;(4)Four types of favorable exploration targets with exploration potential were developed in the western Central Depression which are structural traps neighboring to the source,stratigraphic traps neighboring to the source,shale-gas type within the source,and structural traps within the source.Great attention should be paid to these targets.

Bimetallic In_(2)O_(3)/Bi_(2)O_(3) Catalysts Enable Highly Selective CO_(2) Electroreduction to Formate within Ultra-Broad Potential Windows

CO_(2)electrochemical reduction reaction(CO_(2)RR)to formate is a hopeful pathway for reducing CO_(2)and producing high-value chemicals,which needs highly selective catalysts with ultra-broad potential windows to meet the industrial demands.Herein,the nanorod-like bimetallic ln_(2)O_(3)/Bi_(2)O_(3)catalysts were successfully synthesized by pyrolysis of bimetallic InBi-MOF precursors.The abundant oxygen vacancies generated from the lattice mismatch of Bi_(2)O_(3)and ln_(2)O_(3)reduced the activation energy of CO_(2)to*CO_(2)·^(-)and improved the selectivity of*CO_(2)·^(-)to formate simultaneously.Meanwhile,the carbon skeleton derived from the pyrolysis of organic framework of InBi-MOF provided a conductive network to accelerate the electrons transmission.The catalyst exhibited an ultra-broad applied potential window of 1200 mV(from-0.4 to-1.6 V vs RHE),relativistic high Faradaic efficiency of formate(99.92%)and satisfactory stability after 30 h.The in situ FT-IR experiment and DFT calculation verified that the abundant oxygen vacancies on the surface of catalysts can easily absorb CO_(2)molecules,and oxygen vacancy path is dominant pathway.This work provides a convenient method to construct high-performance bimetallic catalysts for the industrial application of CO_(2)RR.

A COMPACT EMBEDDING RESULT FOR NONLOCAL SOBOLEV SPACES AND MULTIPLICITY OF SIGN-CHANGING SOLUTIONS FOR NONLOCAL SCHRÖDINGER EQUATIONS

For any s∈(0,1),let the nonlocal Sobolev space X^(s)(ℝ^(N))be the linear space of Lebesgue measure functions fromℝN toℝsuch that any function u in X^(s)(ℝ^(N))belongs to L2(ℝN)and the function(x,y)\longmapsto\big(u(x)-u(y)\big)\sqrt{K(x-y)}is in L2(ℝN,ℝN).First,we show,for a coercive function V(x),the subspace E:=\bigg\{u\in X^s(\mathbb{R}^N):\int_{\mathbb{R}^N}V(x)u^2{\rm d}x<+\infty\bigg\}of X^(s)(ℝ^(N))is embedded compactly into L^(p)(ℝ^(N))for p\in[2,2_s^*),where 2_s^*is the fractional Sobolev critical exponent.In terms of applications,the existence of a least energy sign-changing solution and infinitely many sign-changing solutions of the nonlocal Schrödinger equation-{\cal{L}_K}u+V(x)u=f(x,u),\x\in\\mathbb{R}^N are obtained,where-{\cal{L}_K}is an integro-differential operator and V is coercive at infinity.

Probing the electric double layer structure at nitrogen-doped graphite electrodes by constant-potential molecular dynamics simulations

Electric double layer(EDL)is a critical topic in electrochemistry and largely determines the working performance of lithium batteries.However,atomic insights into the EDL structures on heteroatom-modified graphite anodes and EDL evolution with electrode potential are very lacking.Herein,a constant-potential molecular dynamics(CPMD)method is proposed to probe the EDL structure under working conditions,taking N-doped graphite electrodes and carbonate electrolytes as an example.An interface model was developed,incorporating the electrode potential and atom electronegativities.As a result,an insightful atomic scenario for the EDL structure under varied electrode potentials has been established,which unveils the important role of doping sites in regulating both the EDL structures and the following electrochemical reactions at the atomic level.Specifically,the negatively charged N atoms repel the anions and adsorb Li~+at high and low potentials,respectively.Such preferential adsorption suggests that Ndoped graphite can promote Li~+desolvation and regulate the location of Li~+deposition.This CPMD method not only unveils the mysterious function of N-doping from the viewpoint of EDL at the atomic level but also applies to probe the interfacial structure on other complicated electrodes.

Mass Increase with Strong and Gravitational Potentials, and Mass Defect with Electromagnetic Potential

The proposal is “mass increases due to strong and gravitational potentials, while it decreases due to Electromagnetic potential”. This proposal explains the big difference in mass between hadrons (protons, neutrons, & mesons) and their components (quarks), mass difference between nucleus and its individual components (protons and neutrons), massless of gamma photons, abnormal masses of mesons and bosons, and the excess in galaxy masses (dark matter). Also, this proposal shows the exact relation between mass and energy: Strong Potential=−3.04mc2| Electric Potential |=−5.57×10−3mc2Gravitational Potential=−1.22×10−7mc2where m represents the excess in mass due to strong potential, or gravitational potential and represents the decrease in mass due to electromagnetic potential. Released energy here equals potential energy and doesn’t equal decrease in mass using the formula E = mc2. Released energy is transferred to heat, photons, kinetic energy… Finally, proposal will try to describe the relation between photon energy and mass of its components using the general equation of kinetic energy: Photon Energy=1/2mc2m is the sum of the individual masses of its components, while the total mass of photon is zero.

Krüppel-like factor 2(KLF2),a potential target for neuroregeneration

Neurological disorders and injuries lead to the impairment or depletion of neurons in terms of quantity,structure,or function,resulting in the loss of cognitive,emotional,and physical abilities in human beings.This,in turn,accompanies the shortfall of valuable human resources and economic potential,causing a detriment to society.Addressing these challenges,therefore,becomes imperative not only from a humanitarian perspective but also as a means of preserving human capital and bolstering economic prosperity.

Mitochondria–cGAS–STING axis is a potential therapeutic target for senescence-dependent inflammaging-associated neurodegeneration

The word “senescence” comes from the Latin senescens, meaning “to begin to age”, and is characterized by a long-lasting but reversible block in proliferation, resulting from stress-induced cell cycle arrest of previously replication-competent cells.

Median Nerve Somatosensory Evoked Potentials in Patients with Chiari Malformation

Abnormal SEP reflects dysfunction of the medial lemniscus and posterior cervical cord. These structures are likely to be affected in Chiari malformation. Therefore, SEP abnormalities may provide valuable information in patients with CM. However, the consistency of SEP abnormality or normality with the damage is a matter of research. Knowing whether median nerve somatosensory evoked potential (SEP) is useful in revealing subclinical damage in patients with Chiari malformation is important in the treatment and follow-up plan of the disease. The aim of this study was to investigate the relationship between median nerve SEP values and the severity of cerebellar ectopia in patients with Chiari type 1 malformation. Median nerve SEP values were obtained from 30 healthy individuals and 146 individuals with Chiari malformation. The cerebellar ectopia degree and McRae line length were measured. SEP values were not significantly different between groups. The McRae line was found to be significantly shorter in the control group than in the Chiari malformation group (p = 0.031). There was no correlation between the degree of cerebellar ectopia and the length of the McRae line (r = 0.002, p = 0.979). Neither cerebellar ectopy degree nor McRae line length had a relationship with SEP values (r = -0.153, p = 0.066;r = -0.056, p = 0.500, respectively). There was no difference in cerebellar ectopy degree or SEP values between the groups with cerebellar ectopy with and without a syrinx (p = 0.899;p = 0.080, respectively). Likewise, McRae line length was not found to be related to the presence of a syrinx (p = 0.139). Median nerve SEP examination was not beneficial for diagnosing asymptomatic-oligosymptomatic Chiari malformation as a subclinical injury, whether accompanied by syringomyelia or not.

THE SMOOTHING EFFECT IN SHARP GEVREY SPACE FOR THE SPATIALLY HOMOGENEOUS NON-CUTOFF BOLTZMANN EQUATIONS WITH A HARDPOTENTIAL

In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.

Evaluation of Hydrocarbon Potential Using AVO Analysis in the FORMAT Field, Niger Delta Basin, Nigeria

The study involved the evaluation of the hydrocarbon potential of FORMAT Field, coastal swamp depobelt Niger delta, Nigeria to obtain a more efficient reservoir characterization and fluid properties identification. Despite advances in seismic data interpretation using traditional 3D seismic data interpretation, obtaining adequate reservoir characteristics at the finest level had proved very challenging with often disappointing results. A method that integrates the amplitude variation with offfset (AVO) analysis is hereby proposed to better illuminate the reservoir. The Hampson Russell 10.3 was used to integrate and study the available seismic and well data. The reservoir of interest was delineated using the available suite of petrophysical data. This was marked by low gamma ray, high resistivity, and low acoustic impedance between a true subsea vertical depth (TVDss) range of 10,350 - 10,450 ft. The AVO fluid substitution yielded a decrease in the density values of pure gas (2.3 - 1.6 g/cc), pure oil (2.3 - 1.8 g/cc) while the Poisson pure brine increased (2.3 to 2.8 g/cc). Result from FORMAT 26 plots yielded a negative intercept and negative gradient at the top and a positive intercept and positive gradient at the Base which conforms to Class III AVO anomaly. FORMAT 30 plots yielded a negative intercept and positive gradient at the top and a positive intercept and negative gradient at the Base which conforms to class IV AVO anomaly. AVO attribute volume slices decreased in the Poisson ratio (0.96 to - 1.0) indicating that the reservoir contains hydrocarbon. The s-wave reflectivity and the product of the intercept and gradient further clarified that there was a Class 3 gas sand in the reservoir and the possibility of a Class 4 gas sand anomaly in that same reservoir.

Thermal conductivity of GeTe crystals based on machine learning potentials

GeTe has attracted extensive research interest for thermoelectric applications.In this paper,we first train a neuroevolution potential(NEP)based on a dataset constructed by ab initio molecular dynamics,with the Gaussian approximation potential(GAP)as a reference.The phonon density of states is then calculated by two machine learning potentials and compared with density functional theory results,with the GAP potential having higher accuracy.Next,the thermal conductivity of a GeTe crystal at 300 K is calculated by the equilibrium molecular dynamics method using both machine learning potentials,and both of them are in good agreement with the experimental results;however,the calculation speed when using the NEP potential is about 500 times faster than when using the GAP potential.Finally,the lattice thermal conductivity in the range of 300 K-600 K is calculated using the NEP potential.The lattice thermal conductivity decreases as the temperature increases due to the phonon anharmonic effect.This study provides a theoretical tool for the study of the thermal conductivity of GeTe.

Hepatic perivascular epithelioid cell tumors:Benign,malignant,and uncertain malignant potential

In 2013,the World Health Organization defined perivascular epithelioid cell tumor(PEComa)as“a mesenchymal tumor which shows a local association with vessel walls and usually expresses melanocyte and smooth muscle markers.”This generic definition seems to better fit the PEComa family,which includes angiomyolipoma,clear cell sugar tumor of the lung,lymphangioleiomyomatosis,and a group of histologically and immunophenotypically similar tumors that include primary extrapulmonary sugar tumor and clear cell myomelanocytic tumor.Clear cell tumors with this immunophenotypic pattern have also had their malignant variants described.When localizing to the liver,preoperative radiological diagnosis has proven to be very difficult,and most patients have been diagnosed with hepatocellular carcinoma,focal nodular hyperplasia,hemangioma,or hepatic adenoma based on imaging findings.Examples of a malignant variant of the liver have been described.Finally,reports of malignant variants of these lesions have increased in recent years.Therefore,we support the use of the Folpe criteria,which in 2005 established the criteria for categorizing a PEComa as benign,malignant,or of uncertain malignant potential.Although they are not considered ideal,they currently seem to be the best approach and could be used for the categorization of liver tumors.

Plasma potential measurements using an emissive probe made of oxide cathode

A novel emissive probe consisting of an oxide cathode coating is developed to achieve a low operating temperature and long service life.The properties of the novel emissive probe are investigated in detail,in comparison with a traditional tungsten emissive probe,including the operating temperature,the electron emission capability and the plasma potential measurement.Studies of the operating temperature and electron emission capability show that the tungsten emissive probe usually works at a temperature of 1800 K-2200 K while the oxide cathode emissive probe can function at about 1200 K-1400 K.In addition,plasma potential measurements using the oxide cathode emissive probe with different techniques have been accomplished in microwave electron cyclotron resonance plasmas with different discharge powers.It is found that a reliable plasma potential can be obtained using the improved inflection point method and the hot probe with zero emission limit method,while the floating point method is invalid for the oxide cathode emissive probe.