Point Charge between Two Grounded and Conducting Planes Forming a 60°Angle and for Yukawa’s Potential and Coulomb’s Potential

For a point charge between two grounded conductor planes forming a 60° angle, the potential and electric field generated by point charge for Yukawa’s potential (e-μr/r) and Coulomb’s potential (1/r) are modeled and simulated. The expression for the potential that generalizes the cases discussed in López-Mariño, M. and Trujillo Caballero, J. (2017) Point Charges and Conducting Planes for Yukawa’s Potential and Coulomb’s Potential. Journal of Electromagnetic Analysis and Applications, 9, 135-146. https://doi.org/10.4236/jemaa.2017.910012 is presented. Graphs for the potential and electric field for both cases are showed using Maple, that of Coulomb and that of Yukawa for different values of μ . The purpose of this work is to offer students a practical guide for problem analysis of electrostatics using Maple’s capabilities as a computational tool.

Point Charges and Conducting Planes for Yukawa’s Potential and Coulomb’s Potential

In this work, we modeled and simulated the electric potential generated by point charges in the region of grounded conductor planes for Yukawa potential (e−μ/r) and Coulomb potential (1/r). We show the symbolic expression for the electric potential and some graphs for it and for the electric field with different values of μ. We observe that the electric potential decreases as the value of μ increases and that does not allow all the charge to be distributed on the surface of the conductor.

Dirac equation for the Hulthén potential within the Yukawa-type tensor interaction

Using the Nikiforov-Uvarov （NU） method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthen potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number K. We deduce the energy eigenvalue equations and corresponding upper- and lower-spinor wave functions in both the pseudospin and spin symmetry cases. Numerical results of the energy eigenvalue equations and the upper- and lower-spinor wave functions are presented to show the effects of the external potential and particle mass parameters as well as pseudospin and spin symmetric constants on the bound-state energies and wave functions in the absence and presence of the tensor interaction.

The Yukawa potential in semirelativistic formulation via supersymmetry quantum mechanics

We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation （SSE） with the Yukawa potential via the supersymmetric quantum mechanics （SUSYQM） for arbitrary quantum numbers. Useful figures and tables are also included.

Approximate solution of the spin-one Duffin-Kemmer-Petiau(DKP) equation under a non-minimal vector Yukawa potential in(1+1)-dimensions

We solve the Duffin-Kemmer-Petiau （DKP） equation with a non-minimal vector Yukawa potential in （1＋1）- dimensional spa^e-time for spin-1 particles. The Nikiforov Uvarov method is used in the calculations, and the eigen- functions as well as the energy eigenvalues are obtained in a proper Pekeris-type approximation.

Spinless particles in the field of unequal scalar vector Yukawa potentials

We present analytical bound state solutions of the spin-zero Klein–Gordon （KG） particles in the field of unequal mix-ture of scalar and vector Yukawa potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary l-state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a simple shortcut of the Nikiforov–Uvarov （NU） method. Further, we solve the KG–Yukawa problem for its exact numerical energy eigenvalues via the amplitude phase （AP） method to test the accuracy of the present solutions found by using the NU method. Our numerical tests using energy calculations demonstrate the existence of inter-dimensional degeneracy amongst the energy states of the KG–Yukawa problem. The dependence of the energy on the dimension D is numerically discussed for spatial dimensions D = 2–6.

Approximate Analytical Solution of the Yukawa Potential with Arbitrary Angular Momenta

The Yukawa potential is often used to compute bound-state normalizations and energy levels of neutral atoms.By using the generalized parametric Nikiforov–Uvarov method,we obtain approximate analytical solutions of the radial Schrödinger equation for the Yukawa potential.The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms.Some numerical results are presented and show that these results are in good agreement with those obtained previously by other methods.Also,we find the energy levels of the familiar pure Coulomb potential energy levels when the screening parameter of the Yukawa potential goes to zero.

Non-Relativistic Bound State Solutions of Modified Quadratic Yukawa plus <i>q</i>-Deformed Eckart Potential

We have obtained approximate bound state solutions of Schr&#246;dinger wave equation with modified quadratic Yukawa plus q-deformed Eckart potential Using Parametric Nikiforov-Uvarov (NU) method. However, we obtained numerical energy eigenvalues and un-normalized wave function using confluent hypergeometric function (Jacobi polynomial). With some modifications, our potential reduces to a well-known potential such as Poschl-Teller and exponential inversely quadratic potential. Numerical bound state energies were carried out using a well-designed Matlab algorithm while the plots were obtained using origin software. The result obtained is in agreement with that of the existing literature.

Comments on“Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential”[Chin. Phys.Lett.34(2017)110301]

Some problems with the article by Oluwadare and Oyewumi[Chin.Phys.Lett.34(2017)110301]are discussed.The previously proposed solution of the Schrödinger wave equation in the generalized inverse quadratic Yukawa potential is unsatisfactory for a number of reasons.

Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential

A bound state solution is a quantum state solution of a particle subjected to a potential such that the particle＇s energy is less than the potential at both negative and positive infinity. The particle＇s energy may also be negative as the potential approaches zero at infinity. It is characterized by the discretized eigenvalues and eigenfunctions, which contain all the necessary information regarding the quantum systems under consideration. The bound state problems need to be extended using a more precise method and approximation scheme. This study focuses on the non-relativistic bound state solutions to the generalized inverse quadratic Yukawa potential. The expression for the non-relativistic energy eigenvalues and radial eigenfunctions are derived using proper quantization rule and formula method, respectively. The results reveal that both the ground and first excited energy eigenvalues depend largely on the angular momentum numbers, screening parameters, reduced mass, and the potential depth. The energy eigenvalues, angular momentum numbers, screening parameters, reduced mass, and the potential depth or potential coupling strength determine the nature of bound state of quantum particles. The explored model is also suitable for explaining both the bound and continuum states of quantum systems.

SHUBIN REGULARITY FOR THE RADIALLY SYMMETRIC SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITH DEBYE-YUKAWA POTENTIAL

In this work, we study the Cauchy problem for the radially symmetric spatially homogeneous Boltzmann equation with Debye-Yukawa potential. We prove that this Cauchy problem enjoys the same smoothing effect as the Cauchy problem defined by the evolution equation associated to a fractional logarithmic harmonic oscillator. To be specific, we can prove the solution of the Cauchy problem belongs to Shubin spaces.

China’s Potential Economic Growths during 2015-2025 under Different Scenarios~

China has entered a crucial period of further growth and restructuring that will last until 2025. Based on a review of the major factors affecting China＇s potential economic growth, this paper has created an integrated economic system model consisting of system dynamics, econometrics, and input-output for the forecast of China＇s economic size and structure by 2025. Analysis shows that prior to 2025, China will be able to maintain a potential annual economic growth rate of 5.7%-7.2%. Faced with an international environment of a possible slowdown of advanced economies and diminishing demographic dividends, China needs to further expedite its urbanization process, enhance R＆D and education spending, increase total factor productivity （TFP）, vigorously develop the tertiary sector, and expand consumption in order to achieve the optimistically estimated growth of 6.6%-7.4% during the period of 2015-2025. Economic growth should be accompanied by the upgrade of industry structure and improvement of investment and consumption structures.

Size dependency and potential field influence on deriving mechanical properties of carbon nanotubes using molecular dynamics

A thorough understanding on the mechanical properties of carbon nanotube （CNT） is essential in extending the advanced applications of CNT based systems. However, conducting experiments to estimate mechanical properties at this scale is extremely challenging. Therefore, development of mechanistic models to estimate the mechanical properties of CNTs along with the integration of existing continuum mechanics concepts is critically important. This paper presents a comprehensive molecular dynamics simulation study on the size dependency and potential function influence of mechanical properties of CNT. Commonly used reactive bond order （REBO） and adaptive intermolecular reactive bond order （A1REBO） potential functions were considered in this regard. Young＇s modulus and shear modulus of CNTs are derived by integrating classical continuum mechanics concepts with molecular dynamics simulations. The results indicate that the potential function has a significant influence on the estimated mechanical properties of CNTs, and the influence of potential field is much higher when studying the torsional behaviour of CNTs than the tensile behaviour.

Momentum Eigensolutions of Feinberg-Horodecki Equation with Time-Dependent Screened Kratzer-Hellmann Potential

We obtain an approximate value of the quantized momentum eigenvalues, Pn, together with the space-like coherent eigenvectors for the space-like counterpart of the Schrödinger equation, the Feinberg-Horodecki equation, with a screened Kratzer-Hellmann potential which is constructed by the temporal counterpart of the spatial form of this potential. In addition, we got exact eigenvalues of the momentum and the eigenstates by solving Feinberg-Horodecki equation with Kratzer potential. The present work is illustrated with three special cases of the screened Kratzer-Hellman potential: the time-dependent screened Kratzer potential, time-dependent Hellmann potential and, the time-dependent screened Coulomb potential.

Daikenchuto (Da-Jian-Zhong-Tang) ameliorates intestinal fibrosis by activating myofibroblast transient receptor potential ankyrin 1 channel

AIM To investigate the anti-fibrotic effects of the traditional oriental herbal medicine Daikenchuto(DKT) associated with transient receptor potential ankyrin 1(TRPA1) channels in intestinal myofibroblasts. METHODS Inflammatory and fibrotic changes were detected in a2,4,6-trinitrobenzenesulfonic acid(TNBS) chronic colitis model of wild-type and TRPA1-knockout(TRPA1-KO) mice via pathological staining and immunoblotting analysis.Ca^(2+) imaging experiments examined the effects of DKT and its components/ingredients on intestinal myofibroblast(In Myo Fib) cell TRPA1 channel function.Profibrotic factors and transforming growth factor (TGF) -β1-associated signaling were tested in an In Myo Fib cell line by q PCR and immunoblotting experiments.Samples from non-stenotic and stenotic regions of the intestines of patients with Crohn’s disease (CD) were used for pathological analysis. RESULTS Chronic treatment with TNBS caused more severe inflammation and fibrotic changes in TRPA1-KO than in wild-type mice.A one-week enema administration of DKT reduced fibrotic lesions in wild-type but not in TRPA1-KO mice.The active ingredients of DKT,i.e.,hydroxyα-sanshool and 6-shogaol,induced Ca^(2+) influxes in In Myo Fib,and this was antagonized by co-treatment with a selective TRPA1 channel blocker,HC-030031.DKT counteracted TGF-β1-induced expression of TypeⅠcollagen andα-smooth muscle actin (α-SMA) ,which were accompanied by a reduction in the phosphorylation of Smad-2 and p38-mitogen-activated protein kinase (p38-MAPK) and the expression of myocardin.Importantly,24-h incubation with a DKT active component Japanese Pepper increased the m RNA and protein expression levels of TRPA1 in In Myo Fibs,which in turn negatively regulated collagen synthesis.In the stenotic regions of the intestines of CD patients,TRPA1 expression was significantly enhanced.CONCLUSION The effects of DKT on the expression and activation of the TRPA1 channel could be advantageous for suppressing intestinal fibrosis,and benefit inflammatory bowel disease treatment.

The therapeutic potential of mesenchymal stem cells in Alzheimer's disease:converging mechanisms

Mesenchymal stem cells （MSCS） are pluripotent stem cells isolated from various tissues, but mostly from bone marrow, adipose tissue, and umbilical cord blood. Well known for their mesenchymal lineages differentiation （e.g., bone, cartilage and fat tissues）, it was suggested that MSCs possess plasticity prop- erties enabling them to differentiate into non-mesenchymal lineages. Indeed, several protocols claimed for differentiating MSCs to neurons in vitro, but concern was raised for the ef- fectiveness and in vivo relevance of such differentiation. Thus, though their neurogenic differentiation properties are still in debate, they were nevertheless, suggested as candidates for treat- ing neurodegenerative disorders such as Parkinson＇s diseases, multiple sclerosis and Alzheimer＇s disease （AD）.

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.

From the Green's Function in Tight-Binding Representation to Interatomic Many-body Potentials

In this paper, we deduce the analytical form of many-body interatomic potentials based on the Green's function in tight-binding representation. The many-body potentials are expressed as the functions of the hopping integrals which are the physical origin of cohesion of atoms. For thesimple case of s-valent system, the inversion of the many-body potentials are discussed in detail by using the lattice inversion method.

Bacterial melanin in rat models of Parkinson's disease: a potential neuroprotective strategy

Melanins are widely used in medicine, pharmacology and cosmetics. Different technologies have been used to obtain melanin including： chemical synthesis based on oxidation of tyrosine and its derivatives; extraction from animal materials; alkaline extraction from plant material; and microbiological synthesis. A few number of works have been published that were focused on purification of water insoluble 3,4-dihy- droxy-phenylalanine-melanins （Kukulianskaia et al., 2002）. The majority of synthetic and natural melanins are insoluble in wa- ter that significantly complicates preparation of pharmacolog- ical and cosmetic preparations. Obtaining of low-cost soluble biotechnological melanin can speed up application of melanin in medicine and other fields. For the first time, melanin-syn-thesizing strain with high level of pigment synthesis - Bacillus thuringiensis was obtained. The ecologically safe technology of biosynthesis, isolation and purification of the bacterial melanin has been elaborated.

JTE-522-induced apoptosis in human gastric adenocarinoma cell line AGS cells by caspase activation accompanying cytochrome C release,membrane translocation of Bax and loss of mitochondrial membrane potential

AIM: To investigate the role of the mitochondrial pathway in JTE-522-induced apoptosis and to investigate the relationship between cytochrome C release, caspase activity and loss of mitochondrial membrane potential (Deltapsim). METHODS: Cell culture, cell counting, ELISA assay, TUNEL, flow cytometry, Western blot and fluorometric assay were employed to investigate the effect of JTE-522 on cell proliferation and apoptosis in AGS cells and related molecular mechanism. RESULTS: JTE-522 inhibited the growth of AGS cells and induced the apoptosis. Caspases 8 and 9 were activated during apoptosis as judged by the appearance of cleavage products from procaspase and the caspase activities to cleave specific fluorogenic substrates. To elucidate whether the activation of caspases 8 and 9 was required for the apoptosis induction, we examined the effect of caspase-specific inhibitors on apoptosis. The results showed that caspase inhibitors significantly inhibited the apoptosis induced by JTE-522. In addition, the membrane translocation of Bax and cytosolic release of cytochrome C accompanying with the decrease of the uptake of Rhodamin 123, were detected at an early stage of apoptosis. Furthermore, Bax translocation, cytochrome C release, and caspase 9 activation were blocked by Z-VAD.fmk and Z-IETD-CHO. CONCLUSION: The present data indicate a crucial association between activation of caspases 8, 9, cytochrome C release, membrane translocation of Bax, loss of Deltapsim and JTE-522-induced apoptosis in AGS cells.